Stability of multi-solitons for the derivative nonlinear Schr{ö}dinger equation

Abstract

The nonlinear Schr{ö}dinger equation with derivative cubic nonlinearity admits a family of solitons, which are orbitally stable in the energy space. In this work, we prove the orbital stability of multi-solitons configurations in the energy space, under suitable assumptions on the speeds and frequencies of the composing solitons. The main ingredients of the proof are modulation theory, energy coercivity and monotonicity properties.

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Cited by in corpus (7)

• A sufficient condition for global existence of solutions to a generalized derivative nonlinear Schrödinger equation
• Stability of the traveling waves for the derivative Schrödinger equation in the energy space
• Instability of the solitary waves for the generalized derivative nonlinear Schrödinger equation in the degenerate case
• Stability of the sum of two solitary waves for (gDNLS) in the energy space
• Optimal small data Scattering for the generalized derivative nonlinear Schrödinger equations
• The derivative NLS equation: global existence with solitons
• Instability of degenerate solitons for nonlinear Schrödinger equations with derivative