## Solitons and the Inverse Scattering TransformA study, by two of the major contributors to the theory, of the inverse scattering transform and its application to problems of nonlinear dispersive waves that arise in fluid dynamics, plasma physics, nonlinear optics, particle physics, crystal lattice theory, nonlinear circuit theory and other areas. A soliton is a localised pulse-like nonlinear wave that possesses remarkable stability properties. Typically, problems that admit soliton solutions are in the form of evolution equations that describe how some variable or set of variables evolve in time from a given state. The equations may take a variety of forms, for example, PDEs, differential difference equations, partial difference equations, and integrodifferential equations, as well as coupled ODEs of finite order. What is surprising is that, although these problems are nonlinear, the general solution that evolves from almost arbitrary initial data may be obtained without approximation. |

### What people are saying - Write a review

We haven't found any reviews in the usual places.

### Contents

1ST in Other Settings | 93 |

Other Perspectives | 151 |

Applications | 275 |

Linear Problems | 351 |

393 | |

415 | |

### Common terms and phrases

action-angle variables algebra amplitude analytic applies asymptotic solution Backlund transformation boundary conditions coefficients conservation laws consider constant corresponding decay defined derivation differential equations dimensional discrete eigenvalues discussed dispersion relation eigenfunctions eigenvalue problem energy integral example expansion exponential finite follows Fourier transform function given group velocity Hamiltonian Hence Hirota infinite initial data interaction internal waves inverse scattering Inverse Scattering Transform J-oo Kadomtsev-Petviashvili equation Kaup KdV equation Kruskal limit linear integral equation linearized dispersion relation linearized problem Manakov matrix method mKdV N-soliton Newell nonlinear evolution equations nonlinear Schrodinger equation obtained ODE's P-type Painleve perturbation potential pseudopotential resonant triads satisfies Satsuma scattering data scattering problem Show sine-Gordon equation singularity solitary wave soliton solutions solitons solvable by 1ST solved by 1ST Substituting surface waves theory Toda lattice unstable upper half plane vanish variables water waves yields zero