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arXiv · 1511.09063

Collision of solitons for a non-homogenous version of the KdV equation

Georgy Omel'yanov
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Abstract

We consider KdV-type equations with $C^1$ nonhomogeneous nonlinearities and small dispersion $\varepsilon$. The first result consists in the conclusion that, in the leading term with respect to $\varepsilon$, the solitary waves in this model interact like KdV solitons. Next it turned out that there exists a very interesting scenario of instability in which the short-wave soliton remains stable whereas a small long-wave part, generated by perturbations of original equation, turns to be unstable, growing and destroying the leading term. At the same time, such perturbation can eliminate the collision of solitons.

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Georgy Omel'yanov. 2015-11-29. Collision of solitons for a non-homogenous version of the KdV equation. https://arxiv.org/abs/1511.09063

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