Chaotic Behaviour of Nonlinear Evolution Equation with Fifth Order Dispersion

Abstract

We have numerically investigated the solution of a nonlinear evolution equation with the second order nonlinearity and the fifth order dispersion. The equation is non-integrable in the sense that the equation has only three conserved quantities. When the initial wave amplitude is small, the solution looks like integrable. In this case, the recurrence of an initial waveform is observed like the solution of the Korteweg-de Vries equation. If the amplitude is increased beyond a certain threshold, the solution depends sensitively on the initial condition. In such a chaotic solution, the recurrence is no longer observed.