Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection

Details Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection Dynamics of soliton-like solutions for slowly varying, generalized gKdV equations: refraction vs. reflection

2010-09-24

arxiv.org/abs/1009.4905v1

SIAM J. Math. Anal. Vol. 44 (2012), No. 1, pp. 1-60

Mathematics

Analysis of PDEs

51 pages, submitted

Scientific paper

10.1137/100809763

In this work we continue the description of soliton-like solutions of some slowly varying, subcritical gKdV equations. In this opportunity we describe, almost completely, the allowed behaviors: either the soliton is refracted, or it is reflected by the potential, depending on its initial energy. This last result describes a new type of soliton-like solution for gKdV equations, also present in the NLS case. Moreover, we prove that the solution is not pure at infinity, unlike the standard gKdV soliton.

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