## Algebraic and spectral methods for nonlinear wave equations |

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### Contents

Point Transformation | 1 |

Higher Order Transformation | 41 |

Recursion Operator and Lax Pair | 82 |

Copyright | |

8 other sections not shown

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### Common terms and phrases

Ablowitz arbitrary function Asano asymptotic B+(x boundary values Cauchy coefficients condition conservation law consider constant construct convergence coordinates defined denotes derivatives differential equations equivalent Euler-Lagrange equation evolution equation Example exists f+(x finite Fredholm determinant Fredholm theory given hence identity independent integral equation integral kernel integral operator introduce invariant manifold invariant solution inverse scattering inverse-scattering method Jost solution KdV equation Lax pair Lemma Let Q Lie algebra linear Manakov mapping Marchenko equation nonlinear equations Note obtain off-diagonal parameter point transformation Poisson bracket potential Q Proof properties Q e CF(0 recursion operator regular relation respect satisfies scattering data scattering problem soliton space spectral problem symmetry vanishes variables vector field yields zero ZS-AKNS system