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