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On the Modified Korteweg–De Vries Equation
Mathematical Physics, Analysis and Geometry, 1999zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Hayashi, Nakao, Naumkin, Pavel
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Boundary Stabilization of the Korteweg-de Vries Equation and the Korteweg-de Vries-Burgers Equation
Acta Applicandae Mathematicae, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Jia, Chaohua, Zhang, Bing-Yu
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In this chapter we study the local well-posedness (LWP) for the initial value problem (IVP) associated to the generalized KdV equation. We discuss the local theory for the KdV equation, the modified KdV equation, and the generalized KdV equations. We also show the sharpness of some of these results.
Felipe Linares, Gustavo Ponce
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Stochastic Korteweg-de Vries Equation
Journal of the Physical Society of Japan, 1983The Korteweg-de Vries equation with external noise is studied. It is shown that a soliton under Gaussian noise satisfies a diffusion equation in transformed coordinates. The deformation of the soliton during the propagation is explicitly obtained. The phenomenon is designated as the diffusion of soliton.
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The Korteweg-de Vries equation and the Burgers equation are derived for a wide class of nonlinear Galilean-invariant systems under the weak-nonlinearity and long-wavelength approximations. The former equation is shown to be a limiting form for nonlinear dispersive systems while the latter is a limiting form for nonlinear dissipative systems.
Su, C.-H., Gardner, Clifford S.
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