## Asymptotic Methods in Nonlinear Wave Theory |

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### Contents

Part I Fundamental singular perturbation methods | 17 |

9 Higher approximations | 40 |

Part H Various asymptotic methods useful | 47 |

Copyright | |

7 other sections not shown

### Common terms and phrases

applied assumed asymptotic behaviour asymptotic expansion Boussinesq equation coefficients complex amplitude constant coordinate denotes dependent derivative expansion method determined dispersion relation dt dx Duffing equation dx dx equa Euler-Lagrange equation exact solution expression first-order Fourier transformation frequency given group velocity independent variables inhomogeneous initial conditions integral introduce inverse scattering KBM method Korteweg-de Vries equation Let us consider linear dispersion relation long waves long-wave approximation lowest-order multiple scales nonlinear dispersive waves nonlinear Schrodinger equation nonlinear wave nonsecularity condition obtain order of approximation partial differential equations perturbation analysis perturbation equations phase velocity PLK method power series procedure quasi-monochromatic wave ray method reduced reductive perturbation method respect result right-hand side satisfied second-order secular-type singular perturbation slow variables small parameter solitary wave soliton solved straightforward Substituting system of equations Taniuti terms proportional tion two-timing variational principle vector VUA0 wave modulation wave propagation wave solution wavenumber wavetrains