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N-soliton solutions for the combined KdV–CDG equation and the KdV–Lax equation
Applied Mathematics and Computation, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Symmetries of the KdV equation and four hierarchies of the integrodifferential KdV equations
Journal of Mathematical Physics, 1994Using 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, 1997zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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Modified approximation for the KdV–Burgers equation
Applied Mathematics and Computation, 2014zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hassan N. A. Ismail +2 more
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Lax equations scattering and KdV
Journal of Mathematical Physics, 2003The 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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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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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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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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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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Applied Mathematics and Computation, 1997
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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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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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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The geometry of the KdV equation
International Journal of Modern Physics A, 1991In this talk I shall give a fairly geometrical account of the main facts about the KdV equation on the circle, explaining in particular how it is related to the group Diff(S1), and why it is a completely integrable Hamiltonian system. In §4 I shall describe the theorem of Drinfeld and Sokolov [1] which shows that the KdV system can be regarded as a ...
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