## Soliton Theory: A Survey of ResultsA coherent introduction to the complete range of soliton theory including Hirota's method and Backlund transformations. Details physical applications of soliton theory with chapters on the peculiar wave patterns of the Andaman Sea, atmospheric phenomena, general relativity and Davydov solitons. Contains testing for full integrability, a discussion of the Painlevé technique, symmetries and conservation law. |

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### Contents

Spectral transforms P J Caudrey | 25 |

Twodimensional spectral transforms P J Caudrey | 55 |

Hirotas method J C Nimmo | 75 |

Backlund transformations in soliton theory C Rogers | 97 |

Why the NLS equation is simultaneously a success | 133 |

The generation and propagation of internal solitons | 152 |

General relativity R K Dodd | 174 |

Soliton models of protein dynamics P S Lomdahl | 208 |

### Common terms and phrases

AKNS amide-I amplitude analytic Andaman Sea arbitrary asymptotic auto-Backlund transformation Backlund transformation bilinear boundary canonical Chapter coefficients commutation complete integrability consider constant construction coordinates corresponding Davydov Davydov solitons defined deformation problem denote dependence derivative differential equations eigenvalues elements energy equa example field equations finite finite-gap flows follows Fordy function generalised given gives Hamiltonian operators Hamiltonian structure Hamiltonian system Hirota Hirota equation infinite integrable systems internal soliton internal waves invariant inverse scattering isospectral KdV equation KdV hierarchy Korteweg-de Vries equation KP equation Krichever Lax equation Lax pair Lett Manakov Math Mathematics matrix method Miura map MKdV N-soliton solution NLS equation non-trivial nonlinear nonlinear evolution equations obtained Painleve Phys physical Poisson bracket poles polynomial potential pulse relations representation resonance satisfies scattering problem Section simple Lie algebras sine-Gordon equation singular solved stationary theorem tion Toda lattice variables vector Zakharov zero