On a model equation of traveling and stationary compactons

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Abstract

We introduce and study a new class of nonlinear dispersive equations: ut + (um)x + [Q (u, ux, ux x)]x = 0, where Q (u, ux, ux x) = q0 (u, ux) ux x + q1 (u, ux) ux2 is the dispersive flux with typical q s being monomials in u and ux (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 ut + (um)x + [ua (∇ u)2 κ2 ub]x = 0 which induces N-dimensional compactons convected in x-direction. Two families of explicit solutions of N-dimensional compactons are also presented.

Original languageEnglish
Pages (from-to)44-50
Number of pages7
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume356
Issue number1
DOIs
StatePublished - 24 Jul 2006

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