Radiation by solitons due to higher-order dispersion

Abstract

We consider the Korteweg–de Vries (KdV) and nonlinear Schrödinger (NS) equations with higher-order derivative terms describing dispersive corrections. Conditions of existence of stationary and radiating solitons of the fifth-order KdV equation are obtained. An asymptotic time-dependent solution to the latter equation, describing the soliton radiation, is found. The radiation train may be in front as well as behind the soliton, depending on the sign of dispersion. The change rate of the soliton due to the radiation is calculated. A modification of the WKB method, that permits one to describe in a simple and general way the radiation of KdV and NS, as well as other types of solitons, is developed. From the WKB approach it follows that the soliton radiation is a result of a tunneling transformation of the nonlinearly self-trapped wave into the free-propagating radiation.