On the soliton dynamics under a slowly varying medium for generalized KdV equations

Details On the soliton dynamics under a slowly varying medium for generalized KdV equations On the soliton dynamics under a slowly varying medium for generalized KdV equations

2009-12-23

arxiv.org/abs/0912.4725v2

Analysis and PDE Vol. 4 (2011), No. 4, 573-638

Mathematics

Analysis of PDEs

Submitted. Corrected some typos, updated references

Scientific paper

10.2140/apde.2011.4-4

We consider the problem of the soliton propagation, in a slowly varying medium, for a generalized Korteweg - de Vries equations (gKdV). We study the effects of inhomogeneities on the dynamics of a standard soliton. We prove that slowly varying media induce on the soliton solution large dispersive effects at large time. Moreover, unlike gKdV equations, we prove that there is no pure-soliton solution in this regime.

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