Journal ArticleDOI
Method for solving the Korteweg-deVries equation
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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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On "new travelling wave solutions" of the KdV and the KdV-Burgers equations
TL;DR: In this article, the Korteweg-de Vries and the Burgers equations were considered using the travelling wave and the general solutions of these equations were presented using the traveling wave.
Journal ArticleDOI
Computation of the direct scattering transform for the nonlinear Schroedinger equation
Guido Boffetta,A. R. Osborne +1 more
TL;DR: In this paper, the authors developed a numerical algorithm for determining the scattering transform spectrum of a nonlinear wave train described by the cubic nonlinear Schroedinger equation (NLS).
Journal ArticleDOI
Weakly non-linear waves in rotating fluids
TL;DR: In this article, the Korteweg-de Vries equation is shown to fail when the tube wall is moved to infinity, and the failure is corrected by singular perturbation procedures.
Journal ArticleDOI
(INVITED) Vortex solitons: Old results and new perspectives
TL;DR: In this article, a comparative review of 2D and 3D solitons is given, with emphasis on states carrying embedded vorticity, and some recent results obtained in studies.
Journal ArticleDOI
Application of the method of simplest equation for obtaining exact traveling-wave solutions for two classes of model PDEs from ecology and population dynamics
TL;DR: In this paper, the traveling-wave solutions of two classes of equations, namely reaction-diffusion and reaction-telegraph, were obtained by the modified method of simplest equation for the cases when the simplest equation is the equation of Bernoulli or Riccati.
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