Periodic finite-genus solutions of the KdV equation are orbitally stable
نویسندگان
چکیده
منابع مشابه
Periodic finite-genus solutions of the KdV equation are orbitally stable
The stability of periodic solutions of partial differential equations has been an area of increasing interest in the last decade. The KdV equation is known to have large families of periodic solutions that are parameterized by hyperelliptic Riemann surfaces. They are generalizations of the famous multi-soliton solutions. We show that all such periodic solutions are orbitally stable with respect...
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Based on some stationary periodic solutions and stationary soliton solutions, one studies the general solution for the relative lax system, and a number of exact solutions to the Korteweg-de Vries (KdV) equation are first constructed by the known Darboux transformation, these solutions include double and triple singular periodic solutions as well as singular soliton solutions whose amplitude d...
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All solutions of the Korteweg – de Vries equation that are bounded on the real line are physically relevant, depending on the application area of interest. Usually, both analytical and numerical approaches consider solution profiles that are either spatially localized or (quasi)periodic. In this paper, we discuss a class of solutions that is a nonlinear superposition of these two cases: their a...
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We derive a Riemann–Hilbert problem satisfied by the Baker-Akhiezer function for the finite-gap solutions of the Korteweg-de Vries (KdV) equation. As usual for Riemann-Hilbert problems associated with solutions of integrable equations, this formulation has the benefit that the space and time dependence appears in an explicit, linear and computable way. We make use of recent advances in the nume...
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ژورنال
عنوان ژورنال: Physica D: Nonlinear Phenomena
سال: 2010
ISSN: 0167-2789
DOI: 10.1016/j.physd.2010.03.005