A review on asymptotic stability of solitary waves in nonlinear dispersive problems in dimension one

Pierre Germain

A review on asymptotic stability of solitary waves in nonlinear dispersive problems in dimension one

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arxiv 2410.04508 v1 pith:RGNVTX3M submitted 2024-10-06 math.AP

Pierre Germain This is my paper · ORCID

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keywords asymptoticnonlinearsolitarystabilitydispersiveequationsfocusmethods

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We review asymptotic stability of solitary waves for nonlinear dispersive equations set on the line. Our focus is threefold: first, the nonlinear Schrodinger equation; second, the notion of full asymptotic stability (which states that perturbations of a solitary wave decompose globally into a solitary wave and a decaying solution); and third, spectral methods. Besides this focus, we summarize the state of the art in a broader context, including nonlinear Klein-Gordon equations, the notion of local asymptotic stability, and virial methods.

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Kink dynamics for the Yang-Mills field in an extremal Reissner-Nordstr\"om black hole
math.AP 2025-01 reject novelty 7.0 of 10

For the Bizon-Kahl Yang-Mills kink in an extremal Reissner-Nordström background, globally bounded perturbations are shown to converge locally in space, and a finite-codimensional stable manifold is built.

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