We analyze the effects of third order dispersion in wavelength division multiplexed dispersion-managed soliton transmission systems using an ordinary differential equations model obtained by the variational method. Interchannel soliton collisions in this type of transmission systems produce...

A weakly nonlinear model is used to study capillary-gravity waves generated by a traveling localized surface pressure distribution. The weakly nonlinear model is a truncation of the potential flow equations in deep water, and includes cubic nonlinear terms. Numerically, solitary waves are shown...

Numerical simulations show that higher order KdV equation under certain conditions has a self-focusing singularity, which means that the solution of the equation blows up in finite time. In this paper, two numerical schemes: the split-step Fourier transform and the pseudospectral methods are...

In this paper, a fractional Korteweg-de Vries equation (KdV for short) with initial condition is introduced by replacing the first order time and space derivatives by fractional derivatives of order α and β with 0α,β≤1, respectively. The fractional derivatives are described in the Caputo...

It is shown that if the dispersion of the KdV equation is replaced by a higher order dispersion ∂xm, where m≥3 is an odd integer, then the critical Sobolev exponent for local well-posedness on the circle does not change. That is, the resulting equation is locally well-posed in Hs(T), s≥−1/2.

Solutions of a boundary value problem for the Korteweg–de Vries equation are approximated numerically using a finite-difference method, and a collocation method based on Chebyshev polynomials. The performance of the two methods is compared using exact solutions that are exponentially small at...