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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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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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On traveling wave solutions to combined KdV–mKdV equation and modified Burgers–KdV equation
Communications in Nonlinear Science and Numerical Simulation, 2009zbMATH Open Web Interface contents unavailable due to conflicting licenses.
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On the Bäcklund Transformations of KDV Equations and Modified KDV Equations
1989Shiing-shen Chern, Chia-kuei Peng
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The Family of the KdV Equations
2009The ubiquitous Korteweg de-Vries (KdV) equation [14] in dimensionless variables reads $$ u_t+ auu_x+ u_{xxx}= 0, $$ (13.1) where subscripts denote partial derivatives. The parameter a can be scaled to any real number, where the commonly used values are a=±1 or a=±6.
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A new method for solving the KdV and KdV-Burgers equations
Il Nuovo Cimento B, 2006In this paper, by using the transformation introduced in Acta Phys. Sin., 53 (2004) 2828, a nonlinear partial differential equation can be reduced to a nonlinear ordinary differential equation, and then solve it by the ansatz technique and with the aid of Mathematica.
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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, 2018Abdul-Majid Wazwaz
exaly
Jacobi elliptic function solutions for a two-mode KdV equation
Journal of King Saud University - Science, 2019Marwan Alquran
exaly
Rational solutions to a KdV-like equation
Applied Mathematics and Computation, 2015Yi Zhang, Wen-Xiu Ma
exaly