Results 171 to 180 of about 23,327 (208)

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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PSEUDOPOTENTIAL METHOD APPLIED TO KdV EQUATION AND HIGHER DEGREE KdV EQUATION

Acta Mathematica Scientia, 1984
Using the invariance of KdV equation under a Galilean transformation we obtain Newton's equation with the first approximation under the generalized meaning of a weak gravitation field, i.e. \[ (A)\quad \partial^ 2\phi /\partial x'{}^ 2=-\partial V(\phi)/\partial \phi \] where \(V(\phi)=(1/6)\phi^ 3-(1/2)v\phi^ 2-k\phi\) is called pseudopotential.
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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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Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations

Journal of Mathematical Physics, 1994
Using the inverse strong symmetry of the Korteweg–de Vries (KdV) equation on the trivial symmetry and τ0 symmetry, one gets four new sets of symmetries of the KdV equation. These symmetries are expressed explicitly by the multi-integrations of the Jost function of the KdV equation and constitute an infinite dimensional Lie algebra together with two ...
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On a forced modified KdV equation

Physics Letters A, 1997
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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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Modified approximation for the KdV–Burgers equation

Applied Mathematics and Computation, 2014
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Hassan N. A. Ismail, Tamer M. Rageh, Ghada S. E. Salem   +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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Perturbed KdV Equations

2003
In this chapter we study small perturbations of the KdV equation $$ u_t = - u_{xxx} + 6uu_x $$ on the real line with periodic boundary conditions. We consider this equation as an infinite dimensional, integrable Hamiltonian system and subject it to sufficiently small Hamiltonian perturbations.
Thomas Kappeler, Jürgen Pöschel
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On KdV type equations

Applied Mathematics and Computation, 1997
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