The Modified Korteweg-de Vries Equation

It is shown that the Modified Korteweg-de Vries equation can be solved exactly by the “inverse scattering method.” As the special case, the N -soliton solution is obtained explicitly. It is found that N -soliton collision in the Modified Korteweg-de Vries equation is essentially the same as that in the Korteweg-de Vries equation; N -soliton collision is described as the successive collisions of two solitons and there is no effect of multiparticle collisions. Moreover, it is shown that the Modified Korteweg-de Vries equation has new families of the solution.