Stability and asymptotic stability in the energy space of the sum of N solitons for subcritical gKdV equations

2001/12/07 by Yvan Martel, Martel, Yvan, Frank Merle +4 · 3 citations
Mathematics · Physics and Astronomy · #Advanced Mathematical Physics Problems #Nonlinear Waves and Solitons #Numerical methods for differential equations #math.AP

paper · pdf · doi:10.48550/arxiv.math/0112071

arxiv created 2001/12/07 · arxiv updated 2009/11/30

Abstract

We prove in this paper the stability and asymptotic stability in H¹ of a decoupled sum of N solitons for the subcritical generalized KdV equations u_t+(u_xx+u^p)_x=0 (1<p<5). The proof of the stability result is based on energy arguments and monotonicity of local L² norm. Note that the result is new even for p=2 (the KdV equation). The asymptotic stability result then follows directly from a rigidity theorem in [15].

Cited by

• Asymptotic stability of solitary waves for the b-family of equations
• Existence of multi-solitons with any parameters for the 5D energy critical wave equation
• Orbital stability of Benjamin--Ono multisolitons

Related

• Asymptotic stability of solitons of the gKdV equations with general nonlinearity
• Stability in the energy space for chains of solitons of the one-dimensional Gross-Pitaevskii equation
• Refined asymptotics around solitons for gKdV equations
• Multi-soliton solutions for the supercritical gKdV equations
• Instability of solitons - revisited, II: the supercritical Zakharov-Kuznetsov equation