Approximate solution of forced korteweg-de vries equation

Abstract

Several findings on forced solitons generated by the forced Korteweg de Vries equation (fKdV) are discussed in this paper. This equation has lost group symmetries due to the forcing term. The traditional group-theoretical approach can no longer generate analytic solution of solitons, because there are no infinitely many conservation laws. Approximate solution and numerical simulation seem to be the only way to solve fKdV equations. In this paper we show how approximate scheme can be used to solve the fKdV equation and generate uniform forced solitons. A detail derivation of the approximate solution was provided and various profiles of fKdV such as the depth of depression zone; hd, amplitude; as, speed; s and the period; Ts of generation of forced uniform solitons was given.