Modified Korteweg–de Vries surfaces
نویسندگان
چکیده
منابع مشابه
Numerical inverse scattering for the Korteweg–de Vries and modified Korteweg–de Vries equations
Recent advances in the numerical solution of Riemann–Hilbert problems allow for the implementation of a Cauchy initial value problem solver for the Korteweg–de Vries equation (KdV) and the defocusing modified Korteweg–de Vries equation (mKdV), without any boundary approximation. Borrowing ideas from the method of nonlinear steepest descent, this method is demonstrated to be asymptotically accur...
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Abstract We prove local existence and uniqueness of solutions of the focusing modified Korteweg de Vries equation ut+u 2 ux+uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a gener...
متن کاملSupersymmetric Modified Korteweg-de Vries Equation: Bilinear Approach
A proper bilinear form is proposed for the N = 1 supersymmetric modified Korteweg-de Vries equation. The bilinear Bäcklund transformation for this system is constructed. As applications, some solutions are presented for it.
متن کاملNew Positon, Negaton, and Complexiton Solutions for a Coupled Korteweg--de Vries -- Modified Korteweg--de Vries System
On the exact solutions of integrable models, there is a new classification way recently based on the property of associated spectral parameters [1]. Negatons, related to the negative spectral parameter, are usually expressed by hyperbolic functions, and positons are expressed by means of trigonometric functions related to the positive spectral parameters. The so-called complexiton, which is exp...
متن کاملOn Solitary-Wave Solutions for the Coupled Korteweg – de Vries and Modified Korteweg – de Vries Equations and their Dynamics
which can be considered as a coupling between the KdV (with respect to u) and the mKdV (with respect to v) equations. The coupled KdV-mKdV equations were proposed by Kersten and Krasil’shchik [1] and originate from a supersymmetric extension of the classical KdV [2]. It also can be considered as a coupling between the KdV and mKdV equations: By setting v = 0 we obtain the KdV equation ut + uxxx...
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ژورنال
عنوان ژورنال: Journal of Mathematical Physics
سال: 2007
ISSN: 0022-2488,1089-7658
DOI: 10.1063/1.2409523