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

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 Schrödinger 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.

41pages

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Cited by in corpus (2)

• A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation
• Instability of the solitary wave solutions for the genenalized derivative Nonlinear Schrödinger equation in the critical frequency case