Journal ArticleDOI
Method for solving the Korteweg-deVries equation
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TLDR
In this paper, a method for solving the initial value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly asAbstract:
A method for solving the initial-value problem of the Korteweg-deVries equation is presented which is applicable to initial data that approach a constant sufficiently rapidly as $|x|\ensuremath{\rightarrow}\ensuremath{\infty}$. The method can be used to predict exactly the "solitons," or solitary waves, which emerge from arbitrary initial conditions. Solutions that describe any finite number of solitons in interaction can be expressed in closed form.read more
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Journal ArticleDOI
Numerical studies of the stochastic Korteweg-de Vries equation
TL;DR: Numerical solutions of the stochastic Korteweg-de Vries equation for three cases corresponding to additive time-dependent noise, multiplicative space- dependent noise and a combination of the two are presented.
Journal ArticleDOI
Travelling Wave Solutions to the Coupled Discrete Nonlinear SCHRÖDINGER Equations
Chao-Qing Dai,Jie-Fang Zhang +1 more
TL;DR: In this paper, the extended Jacobian elliptic function approach was used to construct seven families of new Jacobian Elliptic function solutions for the coupled discrete nonlinear Schrodinger equations.
Journal ArticleDOI
A second order numerical scheme for the solution of the one-dimensional Boussinesq equation
TL;DR: A predictor–corrector (P-C) scheme is applied successfully to a nonlinear method arising from the use of rational approximants to the matrix-exponential term in a three-time level recurrence relation.
Journal ArticleDOI
On equations of type uxt=F(u,ux) which describe pseudospherical surfaces
Mauro L. Rabelo,Keti Tenenblat +1 more
TL;DR: In this paper, it was shown that an equation uxt=F(u,ux) has a self-Baclund transformation if and only if it describes an η-pseudospherical surface.
Journal ArticleDOI
Existence of solution to Korteweg–de Vries equation in a non-parabolic domain
Yassine Benia,Andrea Scapellato +1 more
TL;DR: In this article, the authors studied the semilinear Korteweg-de Vries equation with time variable coefficients, subject to boundary conditions in a non-parabolic domain.
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