## Nonlinear Science at the Dawn of the 21st CenturyNonlinear science is by now a well established field of research at the interface of many traditional disciplines and draws on the theoretical concepts developed in physics and mathematics. The present volume gathers the contributions of leading scientists to give the state of the art in many areas strongly influenced by nonlinear research, such as superconduction, optics, lattice dynamics, biology and biomolecular dynamics. While this volume is primarily intended for researchers working in the field care, has been taken that it will also be of benefit to graduate students or nonexpert scientist wishing to familiarize themselves with the current status of research. |

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### Contents

I | 1 |

II | 3 |

III | 47 |

IV | 68 |

V | 69 |

VI | 87 |

VII | 103 |

VIII | 121 |

XV | 247 |

XVI | 263 |

XVII | 265 |

XVIII | 293 |

XIX | 307 |

XX | 323 |

XXI | 339 |

XXII | 357 |

### Common terms and phrases

amplitude analytical anharmonic approximation array asymptotic atoms beam boundary conditions breathers cell chain coherent collapse compacton considered constant corresponding coupling dark solitons dependence described discrete dispersion dynamics E.A. Kuznetsov effects Electron energy equation of motion excitations experimental fiber FIGURE finite FK model flux flux-flow fluxon frequency Hamiltonian helix instability integral interaction JETP Josephson effect kinesin kink Kivshar laser lattice layers Lett linear long Josephson junctions magnetic field microwave mode molecules neurons NLS equation noise nonlinear optics nonlinear Schrodinger numerical observed obtained optical fibers oscillations parameter particles perturbation phase phonons Phys physical plasma potential problem propagation protein pulse quantum quasiparticle radiation refractive index resonance self-focusing self-similar simulations sine-Gordon equation singularity solitary waves soliton solutions spatial spin stability stationary structure superconducting switching term theory tion trajectories transverse variable velocity voltage vortex vortices wave guide Yu.S zero