Table of Contents |
| Part I Nonlinear Schrodinger Models: Continuum and Discrete | |
| Solitons and Their Ghosts in PT-Symmetric Systems with Defocusing Nonlinearities | 3 |
1. | Introduction / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 4 |
2. | The Model and Some Analytical Insights / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 5 |
3. | Ground State and Single Dark Soliton / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 8 |
3.1. | Ground State / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 8 |
3.2. | Single Dark Soliton / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 9 |
4. | Multiple Dark Soliton States and Nonlinear PT Phase Transitions / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 13 |
4.1. | Two-Dark-Soliton State / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 13 |
4.2. | Three-Dark-Soliton State / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 17 |
4.3. | Nonlinear PT Phase Transitions / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 19 |
4.4. | The "Free Space" Case / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 21 |
5. | Dark Soliton Dynamics / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 22 |
6. | Ghost States and Their Dynamical Role / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 26 |
7. | Symmetry Breaking and Nonlinear PT Phase Transitions in Two Dimensions / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 30 |
8. | Conclusions / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 40 |
| References / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 41 |
| Coding of Nonlinear States for NLS-Type Equations with Periodic Potential / V. Achilleos, R. Carretero-González, D.J. Frantzeskakis, P.G. Kevrekidis | 43 |
1. | Introduction / A.I. Avramenko, G.L. Alfimov | 43 |
2. | Bounded and Singular Solutions of Stationary States / A.I. Avramenko, G.L. Alfimov | 45 |
2.1. | Some Definitions / A.I. Avramenko, G.L. Alfimov | 45 |
2.2. | Some Statements About Collapsing Points / A.I. Avramenko, G.L. Alfimov | 46 |
3. | Periodic Potential: Poincaré Map / A.I. Avramenko, G.L. Alfimov | 48 |
3.1. | Poincaré Map / G.L. Alfimov, A.I. Avramenko | 48 |
3.2. | Symbolic Dynamics: Theory / A.I. Avramenko, G.L. Alfimov | 49 |
3.3. | Symbolic Dynamics: Application / A.I. Avramenko, G.L. Alfimov | 51 |
4. | Steady States with Cosine Potential / A.I. Avramenko, G.L. Alfimov | 52 |
4.1. | Hypothesis 1 / A.I. Avramenko, G.L. Alfimov | 55 |
4.2. | Hypothesis 2 / A.I. Avramenko, G.L. Alfimov | 56 |
4.3. | Hypothesis 3 / A.I. Avramenko, G.L. Alfimov | 57 |
4.4. | Examples / A.I. Avramenko, G.L. Alfimov | 58 |
5. | Conclusion / A.I. Avramenko, G.L. Alfimov | 60 |
| References / A.I. Avramenko, G.L. Alfimov | 60 |
| Nonreciprocal Wave Propagation Through Open, Discrete Nonlinear Schrödinger Dimers / A.I. Avramenko, G.L. Alfimov | 63 |
1. | Introduction / Giulio Casati, Stefano Lepri | 63 |
2. | The Model / Giulio Casati, Stefano Lepri | 65 |
3. | Stability of Scattering Solutions / Giulio Casati, Stefano Lepri | 68 |
4. | Scattering of Wave Packets / Giulio Casati, Stefano Lepri | 71 |
5. | Summary and Conclusions / Giulio Casati, Stefano Lepri | 72 |
| References / Giulio Casati, Stefano Lepri | 74 |
| Breather Solutions of the Discrete p-Schrödinger Equation / Giulio Casati, Stefano Lepri | 77 |
1. | Introduction and Main Results / Yuli Starosvetsky, Guillaume James | 78 |
2. | Two-Dimensional Mappings Equivalent to the Stationary DpS Equation / Yuli Starosvetsky, Guillaume James | 81 |
2.1. | Force Variables / Yuli Starosvetsky, Guillaume James | 82 |
2.2. | Mixed Variables / Yuli Starosvetsky, Guillaume James | 83 |
3. | Stable and Unstable Manifolds / Yuli Starosvetsky, Guillaume James | 84 |
3.1. | Heuristics / Yuli Starosvetsky, Guillaume James | 85 |
3.2. | Stable Manifold Theorem / Yuli Starosvetsky, Guillaume James | 85 |
3.3. | Stable and Unstable Manifolds for the Maps M, T, F / Yuli Starosvetsky, Guillaume James | 87 |
4. | Homoclinic Solutions of the Stationary DpS Equation / Yuli Starosvetsky, Guillaume James | 90 |
4.1. | Homoclinic Solutions of Generalized DNLS Equations / Yuli Starosvetsky, Guillaume James | 90 |
4.2. | Application to the DpS Equation / Yuli Starosvetsky, Guillaume James | 93 |
5. | Analytical Approximations of Stable and Unstable Manifolds / Yuli Starosvetsky, Guillaume James | 96 |
5.1. | Method of Local Approximation and Backward Iterates / Yuli Starosvetsky, Guillaume James | 97 |
5.2. | Continuum Limit for Weak Nonlinearities / Yuli Starosvetsky, Guillaume James | 103 |
6. | Breather Stability and Mobility / Yuli Starosvetsky, Guillaume James | 107 |
7. | Discussion / Yuli Starosvetsky, Guillaume James | 112 |
| References / Yuli Starosvetsky, Guillaume James | 114 |
| Part II Bose-Einstein Condensates (BECs) and Nonlinear Optics / Yuli Starosvetsky, Guillaume James | |
| Fragmentation of a Bose-Einstein Condensate Through Periodic Modulation of the Scattering Length / Yuli Starosvetsky, Guillaume James | 119 |
1. | Introduction / Alexandru I. Nicolin, Antun Bala[ž] | 119 |
2. | Classification of Density Waves / Alexandru I. Nicolin, Antun Bala[ž] | 121 |
3. | Results and Discussion / Alexandru I. Nicolin, Antun Bala[ž] | 123 |
4. | Conclusions / Alexandru I. Nicolin, Antun Bala[ž] | 127 |
| References / Alexandru I. Nicolin, Antun Bala[ž] | 128 |
| Contact Intensity and Extended Hydrodynamics in the BCS-BEC Crossover / Alexandru I. Nicolin, Antun Bala[ž] | 131 |
1. | Contact Intensity / Luca Salasnich | 131 |
1.1. | Uniform Superfluid Fermi Gas at Zero Temperature / Luca Salasnich | 133 |
1.2. | Contact Intensity in the BCS-BEC Crossover / Luca Salasnich | 134 |
1.3. | Trapped Superfluid Fermi Gas / Luca Salasnich | 135 |
2. | Extended Superfluid Hydrodynamics / Luca Salasnich | 137 |
2.1. | Extended Hydrodynamics in Terms of Goldstone Field / Luca Salasnich | 140 |
2.2. | Application: The Unitary Fermi Gas / Luca Salasnich | 141 |
2.3. | Nonlinear Sound Waves, Static Response Function and Structure Factor / Luca Salasnich | 142 |
3. | Conclusions / Luca Salasnich | 145 |
| References / Luca Salasnich | 145 |
| N-Soliton Interactions for the Manakov System: Effects of External Potentials / Luca Salasnich | 147 |
1. | Introduction / M.D. Todorov, V.S. Gerdjikov | 147 |
2. | Preliminaries / M.D. Todorov, V.S. Gerdjikov | 150 |
2.1. | Derivation of the CTC as a Model for the Soliton Interaction of VNLS Systems / M.D. Todorov, V.S. Gerdjikov | 150 |
3. | Effects of the Polarization Vectors on the Soliton Interaction / M.D. Todorov, V.S. Gerdjikov | 153 |
4. | Derivation of the PCTC as a Model for the Soliton Interactions / M.D. Todorov, V.S. Gerdjikov | 155 |
5. | Comparison of the PCTC with the Perturbed Manakov Model / M.D. Todorov, V.S. Gerdjikov | 158 |
5.1. | The Periodic Potentials / M.D. Todorov, V.S. Gerdjikov | 158 |
5.2. | The Quadratic Potentials / M.D. Todorov, V.S. Gerdjikov | 159 |
5.3. | The Quartic Potentials / M.D. Todorov, V.S. Gerdjikov | 161 |
6. | Discussion / V.S. Gerdjikov, M.D. Todorov | 164 |
7. | Conclusions / M.D. Todorov, V.S. Gerdjikov | 165 |
| References / M.D. Todorov, V.S. Gerdjikov | 166 |
| Wave Modes Trapped in Rotating Nonlinear Potentials / M.D. Todorov, V.S. Gerdjikov | 171 |
1. | Introduction / Yongyao Li, Boris A. Malomed, Wei Pang | 172 |
2. | The Model / Yongyao Li, Boris A. Malomed, Wei Pang | 174 |
3. | Numerical Results / Yongyao Li, Boris A. Malomed, Wei Pang | 176 |
3.1. | The Classification of Trapped Modes / Yongyao Li, Boris A. Malomed, Wei Pang | 176 |
3.2. | The Self-Focusing Nonlinearity / Yongyao Li, Boris A. Malomed, Wei Pang | 177 |
3.3. | The Self-Defocusing Nonlinearity / Wei Pang, Yongyao Li, Boris A. Malomed | 181 |
3.4. | The Alternating Self-Focusing: Self-Defocusing Nonlinear Potential / Yongyao Li, Boris A. Malomed, Wei Pang | 183 |
4. | The Analytical Approach / Yongyao Li, Boris A. Malomed, Wei Pang | 184 |
4.1. | The Two-Mode Approximation / Yongyao Li, Boris A. Malomed, Wei Pang | 184 |
4.2. | The Self-Focusing Nonlinearity / Boris A. Malomed, Wei Pang, Yongyao Li | 184 |
4.3. | The Self-Defocusing Nonlinearity / Yongyao Li, Boris A. Malomed, Wei Pang | 185 |
4.4. | The Alternating Self-Focusing: Self-Defocusing Nonlinearity / Wei Pang, Boris A. Malomed, Yongyao Li | 187 |
5. | Conclusions / Yongyao Li, Boris A. Malomed, Wei Pang | 188 |
| References / Boris A. Malomed, Wei Pang, Yongyao Li | 189 |
| Light Propagation in Two Dimensional Plasmonic Arrays / Yongyao Li, Boris A. Malomed, Wei Pang | 193 |
1. | Introduction / Danhua Wang, Alejandro B. Aceves | 193 |
2. | Theoretical Model and Dispersion Properties: Case 1 / Alejandro B. Aceves, Danhua Wang | 194 |
3. | Theoretical Model and Dispersion Properties: Case 2 / Danhua Wang, Alejandro B. Aceves | 198 |
4. | Modulation Instability / Alejandro B. Aceves, Danhua Wang | 200 |
4.1. | Numerical Simulations / Danhua Wang, Alejandro B. Aceves | 203 |
5. | Solitary Wave Solutions / Alejandro B. Aceves, Danhua Wang | 204 |
6. | Conclusion / Danhua Wang, Alejandro B. Aceves | 207 |
| References / Danhua Wang, Alejandro B. Aceves | 208 |
| Part III Nonlinear Dynamical Lattices / Danhua Wang, Alejandro B. Aceves | |
| Localized Excitations and Anisotropic Directional Ordering in a Two-Dimensional Morse Lattice Model of Cuprate Layers / Danhua Wang, Alejandro B. Aceves | 213 |
1. | Introduction / Manuel G. Velarde, Werner Ebeling, Alexander P. Chetverikov | 213 |
2. | Model Hamiltonian and Visualization of Local and Collective Atom (Lattice Units) Motions / Manuel G. Velarde, Alexander P. Chetverikov, Werner Ebeling | 216 |
3. | Simulation of the Oxygen Dynamics / Werner Ebeling, Manuel G. Velarde, Alexander P. Chetverikov | 220 |
4. | Discussion and Conclusions / Manuel G. Velarde, Werner Ebeling, Alexander P. Chetverikov | 220 |
| References / Werner Ebeling, Manuel G. Velarde, Alexander P. Chetverikov | 223 |
| Variational Approximation to Electron Trapping by Soliton-Like Localized Excitations in One-Dimensional Anharmonic Lattices / Werner Ebeling, Manuel G. Velarde, Alexander P. Chetverikov | 225 |
1. | Introduction / Luis A. Cisneros-Ake, Antonmaria A. Minzoni, Manuel G. Velarde | 225 |
2. | Formulation of the Problem and Numerical Results / Luis A. Cisneros-Ake, Antonmaria A. Minzoni, Manuel G. Velarde | 227 |
3. | Traveling Polaron/Solectron Solutions / Manuel G. Velarde, Luis A. Cisneros-Ake, Antonmaria A. Minzoni | 232 |
4. | Conclusions / Luis A. Cisneros-Ake, Antonmaria A. Minzoni, Manuel G. Velarde | 234 |
| References / Luis A. Cisneros-Ake, Antonmaria A. Minzoni, Manuel G. Velarde | 235 |
| Stability of Mode-Locked Kinks in the AC Driven and Damped Sine-Gordon Lattice / Luis A. Cisneros-Ake, Antonmaria A. Minzoni, Manuel G. Velarde | 237 |
1. | Introduction / Yaroslav Zolotaryuk | 237 |
2. | The Model and Equations of Motion / Yaroslav Zolotaryuk | 238 |
2.1. | The DSG Equation / Yaroslav Zolotaryuk | 238 |
2.2. | Linear Stability and the Floquet Theory / Yaroslav Zolotaryuk | 239 |
3. | Kinks in the High-Frequency Driven DSG Equation / Yaroslav Zolotaryuk | 240 |
3.1. | The Numerical Scheme / Yaroslav Zolotaryuk | 241 |
3.2. | The Existence Diagram / Yaroslav Zolotaryuk | 241 |
3.3. | Floquet Spectrum and the Destabilizing Bifurcations / Yaroslav Zolotaryuk | 244 |
4. | Discussion and Conclusions / Yaroslav Zolotaryuk | 249 |
| References / Yaroslav Zolotaryuk | 250 |
| Spatio-Temporal Dynamics in a Ring of Coupled Pendula: Analogy with Bubbles / Yaroslav Zolotaryuk | 251 |
1. | Introduction / A. Bouakaz, J. Chaline, N. Jiménez, V.J. Sánchez-Morcillo, S. Dos Santos | 252 |
2. | The Ring of Coupled Pendula / A. Bouakaz, J. Chaline, N. Jiménez, V.J. Sánchez-Morcillo, S. Dos Santos | 253 |
2.1. | The Model / V.J. Sánchez-Morcillo, N. Jiménez, J. Chaline, A. Bouakaz, S. Dos Santos | 253 |
2.2. | Experimental Setup / V.J. Sánchez-Morcillo, N. Jiménez, J. Chaline, A. Bouakaz, S. Dos Santos | 254 |
3. | Localized Excitations / V.J. Sánchez-Morcillo, N. Jiménez, J. Chaline, A. Bouakaz, S. Dos Santos | 256 |
3.1. | Lower Cutoff Modes / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 256 |
3.2. | Upper Cutoff Modes / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 258 |
4. | Defect-Induced Localization / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 259 |
5. | Analogy with Gas Bubbles in an Ultrasound Field / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 260 |
6. | Conclusions / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 261 |
| References / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 262 |
| Part IV Quodons and Muscovite Mica / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | |
| Theory of a Quodon Gas with Application to Precipitation Kinetics in Solids Under Irradiation / V.J. Sánchez-Morcillo, N. Jiménez, S. Dos Santos, A. Bouakaz, J. Chaline | 265 |
1. | Introduction / R. Shapovalov, V. Duhinko | 265 |
2. | Gas of Quodons and Its Effect on Reaction Rates in Solids / R. Shapovalov, V. Duhinko | 267 |
2.1. | Gas of Quodons / R. Shapovalov, V. Duhinko | 268 |
2.2. | Modification of Reaction Rates in Solids Under Irradiation / R. Shapovalov, V. Duhinko | 270 |
3. | Modeling of the Precipitation Kinetics Under Irradiation in the Modified Rate Theory / R. Shapovalov, V. Duhinko | 274 |
3.1. | Classical Rate Theory of the Precipitation Kinetics / R. Shapovalov, V. Duhinko | 275 |
3.2. | Quodon-Induced Solubility Limit Change / R. Shapovalov, V. Duhinko | 279 |
3.3. | Quodon-Induced Interfacial Energy Change / R. Shapovalov, V. Duhinko | 282 |
3.4. | Diffusivity of Cu Under Irradiation / R. Shapovalov, V. Duhinko | 283 |
3.5. | Evolution of Cu Precipitates and the Matrix Concentration of Cu Under Electron Irradiation / V. Duhinko, R. Shapovalov | 285 |
4. | Summary / R. Shapovalov, V. Duhinko | 287 |
| References / R. Shapovalov, V. Duhinko | 288 |
| Energy Gain by Discrete Particle Non-linear Lattice Excitations / R. Shapovalov, V. Duhinko | 289 |
1. | Introduction / F.M. Russell | 290 |
2. | Experimental Methods / F.M. Russell | 292 |
3. | Layered Structure Effects / F.M. Russell | 294 |
4. | Molecular Dynamics Simulations of Cascades / F.M. Russell | 296 |
5. | Numerical Modelling in 2D Arrays / F.M. Russell | 298 |
6. | Structure of Non-linear Intrinsic Localised Modes / F.M. Russell | 301 |
7. | Energy Gain by Kink Pulses / F.M. Russell | 304 |
8. | Creation of Coordinated Kink Pulses / F.M. Russell | 306 |
9. | Evidence for Multiple Kink Pulses from Nuclear Scattering 3Q / F.M. Russell | Q7 |
10. | Defect Sweeping / F.M. Russell | 310 |
11. | Inner Structure of Fans / F.M. Russell | 310 |
12. | Discussion / F.M. Russell | 311 |
13. | Conclusion / F.M. Russell | 313 |
| References / F.M. Russell | 314 |
| Supersonic Kinks in Coulomb Lattices / F.M. Russell | 317 |
1. | Introduction / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 318 |
2. | Model Equations / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 319 |
3. | Phonons / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 321 |
4. | Localized Travelling Solutions / Juan F.R. Archilla, Yuriy A. Kosevich, Noé Jiménez, Victor J. Sánchez-Morcillo, Luis M. Garcia-Raffi | 323 |
4.1. | Tail Analysis / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 323 |
4.2. | Oscillating Tails / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 324 |
4.3. | Supersonic Solitons and Kinks / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 325 |
5. | Kink Characteristics Within the Rotating Wave Approximation: Magic Wave Number / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 326 |
6. | Numerical Results / Noé Jiménez, Victor J. Sánchez-Morcillo, Yuriy A. Kosevich, Juan F.R. Archilla, Luis M. Garcia-Raffi | 328 |
7. | Effect of the Interaction with Several Neighbors / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 330 |
8. | Conclusions / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 330 |
| References / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 331 |
| Part V Magnetic Metamaterials / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | |
| Travelling Waves in Nonlinear Magnetic Metamaterials / Juan F.R. Archilla, Yuriy A. Kosevich, Luis M. Garcia-Raffi, Victor J. Sánchez-Morcillo, Noé Jiménez | 335 |
1. | Introduction / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 336 |
2. | Existence Results on Periodic Solutions / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 337 |
3. | Bifurcation Results for Periodic Travelling Waves / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 343 |
4. | Bifurcation Results for Asymptotic Travelling Waves / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 348 |
5. | Numerical Results / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 354 |
| References / J. Diblik, M. Feckan, H. Susanto, V.M. Rothos, M. Pospi[š]il | 357 |
| Stability of Discrete Breathers in Magnetic Metamaterials / J. Diblik, M. Feckan, M. Pospi[š]il, V.M. Rothos, H. Susanto | 359 |
1. | Introduction / Vassilis Rothos, Dmitry Pelinovsky | 359 |
2. | Formalism / Vassilis Rothos, Dmitry Pelinovsky | 360 |
3. | Existence of Multi-site Discrete Breathers / Vassilis Rothos, Dmitry Pelinovsky | 362 |
4. | Stability of Multi-site Breathers / Vassilis Rothos, Dmitry Pelinovsky | 365 |
4.1. | Adjacent Excited Oscillators / Vassilis Rothos, Dmitry Pelinovsky | 366 |
4.2. | Oscillators at Rest Between Excited Oscillators / Vassilis Rothos, Dmitry Pelinovsky | 369 |
5. | Discussion / Vassilis Rothos, Dmitry Pelinovsky | 372 |
| References / Vassilis Rothos, Dmitry Pelinovsky | 374 |
| Part VI Other Nonlinear Models / Vassilis Rothos, Dmitry Pelinovsky | |
| Checking the Validity of Truncating the Cumulant Hierarchy Description of a Small System / Vassilis Rothos, Dmitry Pelinovsky | 377 |
1. | Introduction / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 377 |
2. | The Model / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 379 |
3. | Numerical Simulations / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 380 |
4. | Conclusion / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 386 |
| References / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 387 |
| Shape-Invariant Solitons in Nematic Liquid Crystals: The Influence of Noise / Manuel Morillo, José M. Casado, José Gómez-Ordóñez | 389 |
1. | Introduction / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 389 |
1.1. | Fundamental Solitons / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 389 |
1.2. | Nonlocality / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 390 |
1.3. | Status of the Field / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 390 |
1.4. | Contents of the Chapter / Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic, Milivoj R. Belic | 391 |
2. | The Model / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 391 |
2.1. | Scalar Nonlocal Model of Nematic Liquid Crystals / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 391 |
2.2. | Model Equations / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 392 |
3. | Computations / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 393 |
3.1. | Numerical Procedure / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 393 |
3.2. | Modified Petviashvili Procedure / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 394 |
3.3. | The Stability of Fundamental Solitons / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 395 |
4. | The Influence of Noise / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 397 |
4.1. | The Breathing Problem / Milivoj R. Belic, Milan S. Petrovic, Aleksandra I. Strinic, Najdan B. Aleksic | 397 |
4.2. | Propagation in the Presence of Noise / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 397 |
4.3. | Destructive Influence of Noise / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 399 |
5. | Conclusion / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 400 |
| References / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 400 |
| Conservation Laws of a Family of Reaction-Diffusion-Convection Equations / Milivoj R. Belic, Najdan B. Aleksic, Aleksandra I. Strinic, Milan S. Petrovic | 403 |
1. | Introduction / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 403 |
2. | Formal Lagrangian and Adjoint Equation / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 405 |
3. | Lie Symmetries / M.L. Gandarias, M.S. Bruzón, R. de la Rosa | 406 |
4. | Nonlinear Self-Adjoint Equations / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 409 |
5. | Conservation Laws for a Subclass of Nonlinear Self-Adjoint Equations / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 411 |
6. | Conclusions / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 416 |
| References / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 417 |
| Effects Induced in Complex Biological Systems by High Density Green Photons / M.S. Bruzón, R. de la Rosa, M.L. Gandarias | 419 |
1. | Introduction / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 420 |
2. | Experimental Evidence / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 421 |
2.1. | Mass Spectroscopy / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 422 |
2.2. | Enzyme Reactions / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 424 |
3. | Discusion and Conclusion: A Physical Model / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 426 |
| References / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 427 |
| Index / Sorin Comorosan, Silviu Polosan, Marian Apostol, Elena Ionescu, Ileana Farcasanu, Liliana Paslaru, Irinel Popescu | 429 |