ON THE THEORETICAL BASE OF VISCOUS SHOCK LAYER EQUATIONS AND THE FURTHER DEVELOPMENTS

In this paper, using the reductive perturbation method combined with thePLK method and two-parameter expansion procedure, we treat the problem of head-on colli sion between two solitary waves described by the generalized Korteweg-de Vries equation (the gKdV equation) and obtain its second-order approximate solution. The results show that after the collision, the gKdV solitary waves preserve their profiles and during the collision, the maximal amplitude is the linear superposition of the maximal amplitudes o...