## Abstract

A method for construction of new integrable PDEs, whose properties are related to an asymptotic perturbation expansion with the leading-order term given by an integrable equation, is developed. A new integrable equation is constructed by applying the properly defined Lie-Bäcklund group of transformations to the leading-order equation. The integrable equations related to the Korteweg-de Vries (KdV) equation with higher-order corrections are used to investigate the limits of applicability of the so-called asymptotic integrability concept. It is found that the solutions of the higher-order KdV equations obtained by a near identity transform from the normal form solitary waves cannot, in principle, describe some intrinsic features of the high-order KdV solitons.

Original language | English |
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Pages (from-to) | 1443-1461 |

Number of pages | 19 |

Journal | Nonlinearity |

Volume | 18 |

Issue number | 4 |

DOIs | |

State | Published - 1 Jul 2005 |

## ASJC Scopus subject areas

- Statistical and Nonlinear Physics
- Mathematical Physics
- Physics and Astronomy (all)
- Applied Mathematics