Multi-Peak and Propagation Behavior of M-Shape Solitons in (2 + 1)-Dimensional Integrable Schwarz-Korteweg-de Vries Problem

Korteweg – de Vries equation: solitons and undular bores

The Korteweg – de Vries (KdV) equation is a fundamental mathematical model for the description of weakly nonlinear long wave propagation in dispersive media. It is known to possess a number of families of exact analytic solutions. Two of them: solitons and nonlinear periodic travelling waves – are of particular interest from the viewpoint of fluid dynamics applications as they occur as typical ...

Chiral Solitons in Generalized Korteweg-de Vries Equations

Generalizations of the Korteweg-de Vries equation are considered, and some explicit solutions are presented. There are situations where solutions engender the interesting property of being chiral, that is, of having velocity determined in terms of the parameters that define the generalized equation, with a definite sign.

Numerical solitons of generalized Korteweg-de Vries equations

We propose a numerical method for finding solitary wave solutions of generalized Korteweg-de Vries equations by solving the nonlinear eigenvalue problem on an unbounded domain. The artificial boundary conditions are obtained to make the domain finite. We specially discuss the soliton solutions of the K(m, n) equation and KdV-K(m, n) equation. Furthermore for the mixed models of linear and nonli...

Evolution of randomly perturbed Korteweg-de Vries solitons.

Dispersion management for solitons in a Korteweg-de Vries system.

The existence of "dispersion-managed solitons," i.e., stable pulsating solitary-wave solutions to the nonlinear Schrodinger equation with periodically modulated and sign-variable dispersion is now well known in nonlinear optics. Our purpose here is to investigate whether similar structures exist for other well-known nonlinear wave models. Hence, here we consider as a basic model the variable-co...