Jumps with radiation in models described by the generalized Korteweg-de Vries equation

One of the main types of jumps in reversible systems - jumps with radiation - is investigated using the example of the generalized Korteweg-de Vries e quation. A method of obtaining the relations at the jump without analysing its structure is indicated. Averaged equations and equations fur the centre d simple envelope wave which give a fairly simple and effective description of the jump in the non-local sense are derived. A method For the numerical solution of these equations is described. Methods of investigating the str ucture of the jump are analysed. One of the methods consists of the fact th at the structure of the jump with radiation is regarded as part of a fundam ental type of solitary wave - a multi-soliton with an infinite number of el ementary solitary waves. (C) 2001 Elsevier Science Ltd. All rights reserved .