Results 171 to 180 of about 23,042 (190)

Lax equations scattering and KdV

Journal of Mathematical Physics, 2003
The study of the Korteveg–de Vries (KdV) equation is considered as a special chapter of potential scattering where the dynamic scattering equation is a set of coupled “Lax” equations. With this approach, all points of view and all tools of potential scattering have their counterpart in the standard inverse scattering transform, which appears as a ...
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Classification of Dark Modified KdV Equation

Communications in Theoretical Physics, 2017
Summary: The dark Korteweg-de Vries (KdV) systems are defined and classified by Kupershmidt sixteen years ago. However, there is no other classifications for other kinds of nonlinear systems. In this paper, a complete scalar classification for dark modified KdV (MKdV) systems is obtained by requiring the existence of higher order differential ...
Xiong, Na, Lou, Sen-Yue, Li, Biao, Chen, Yong   +3 more
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A new integrable equation that combines the KdV equation with the negative‐order KdV equation

Mathematical Methods in the Applied Sciences, 2017
In this work, we develop a new integrable equation by combining the KdV equation and the negative‐order KdV equation. We use concurrently the KdV recursion operator and the inverse KdV recursion operator to construct this new integrable equation. We show that this equation nicely passes the Painlevé test.
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On KdV type equations

Applied Mathematics and Computation, 1997
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Forced KdV Equation

1993
In this chapter we study the forced Korteweg-de Vries equation (fKdV) : $$ {u_{t}} + \lambda {u_{x}} + 2\alpha u{u_{x}} + \beta {u_{{xxx}}} = f'(x), - \infty < x < \infty $$ where λ, α 0) such that (a) when λ ≥ λ C the fKdV admits at least two stationary solitary wave solutions and λ = λ C is the turning point of the bifurcation curve;
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Numerical solution of KdV–KdV systems of Boussinesq equations

Mathematics and Computers in Simulation, 2007
Considered here is a Boussinesq system of equations from surface water wave theory. The particular system is one of a class of equations derived and analyzed in recent studies. After a brief review of theoretical aspects of this system, attention is turned to numerical methods for the approximation of its solutions with appropriate initial and boundary
J.L. Bona, V.A. Dougalis, D.E. Mitsotakis   +2 more
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Rational solutions of a differential-difference KdV equation, the Toda equation and the discrete KdV equation

Journal of Physics A: Mathematical and General, 1995
Summary: A series of rational solutions are presented for a differential-difference analogue of the KdV equation, the Toda equation and the discrete KdV equation. These rational solutions are obtained using Hirota's bilinear formalism and Bäcklund transformations. The crucial step is the use of nonlinear superposition formulae.
Hu, Xing-Biao, Clarkson, Peter A.
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Asymptotic attractors of KdV–KSV equations

SeMA Journal, 2018
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N-soliton solutions for the combined KdV–CDG equation and the KdV–Lax equation

Applied Mathematics and Computation, 2008
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On a forced modified KdV equation

Physics Letters A, 1997
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