Numerical study for multi-solitary-wave interaction of regularized long-wave equation

The numerical scheme of the cubic spline difference approximations for the regularized long-wave (RLW) equation, u t + u x + uu x + u xxt = 0, is described with second-order and fourth-order accuracies for the time and spacing variables respectively. The interactions of head-on and catch up collisions of four solitary wave solutions of the RLW equation are examined numerically. The numerical studies show that the interaction collision of the multi-solitons exhibit true solitons behavior, being stable on collision with Korteweg-de Vries (KdV) solitary waves and the oscillatory tail might be by numerical error. The oscillatory tail is appearance but that is within the numerical error of < 2.3%o. Since this error is less than the error of the single solitary waves test program, the RLW solitary waves are considered to behave as true solitons to within the numerical error of the calculation.