Stability of the sum of two solitary waves for (gDNLS) in the energy space

Xingdong Tang; Guixiang Xu

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arXiv · 1702.07858

Stability of the sum of two solitary waves for (gDNLS) in the energy space

Xingdong Tang·Guixiang Xu

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Abstract

In this paper, we continue the study in \cite{MiaoTX:DNLS:Stab}. We use the perturbation argument, modulational analysis and the energy argument in \cite{MartelMT:Stab:gKdV, MartelMT:Stab:NLS} to show the stability of the sum of two solitary waves with weak interactions for the generalized derivative Schr\"{o}dinger equation (gDNLS) in the energy space. Here (gDNLS) hasn't the Galilean transformation invariance, the pseudo-conformal invariance and the gauge transformation invariance, and the case $\sigma>1$ we considered corresponds to the $L^2$-supercritical case.

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Xingdong Tang, Guixiang Xu. 2017-02-25. Stability of the sum of two solitary waves for (gDNLS) in the energy space. https://arxiv.org/abs/1702.07858

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