## Abstract

We introduce and study a new class of nonlinear dispersive equations: u_{t} + (u^{m})_{x} + [Q (u, u_{x}, u_{x x})]_{x} = 0, where Q (u, u_{x}, u_{x x}) = q_{0} (u, u_{x}) u_{x x} + q_{1} (u, u_{x}) u_{x}^{2} is the dispersive flux with typical q^{′} s being monomials in u and u_{x} (which amalgamates all KdV type equations with a monomial nonlinear dispersion) and show that it admits either traveling or stationary compactons. In the second case initial datum given on a compact support evolves into a sequence of stationary compactons, with the spatio-temporal evolution being confined to the initial support. We also discuss an N-dimensional extension u_{t} + (u^{m})_{x} + [u^{a} (∇ u)^{2 κ} ∇^{2} u^{b}]_{x} = 0 which induces N-dimensional compactons convected in x-direction. Two families of explicit solutions of N-dimensional compactons are also presented.

Original language | English |
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Pages (from-to) | 44-50 |

Number of pages | 7 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 356 |

Issue number | 1 |

DOIs | |

State | Published - 24 Jul 2006 |