EXACT TWO-SOLITON SOLUTIONS AND TWO-PERIODIC SOLUTIONS OF THE PERTURBED mKdV EQUATION WITH VARIABLE COEFFICIENTS

摘要

We discuss the Darboux transformation method for a modified Korteweg-de Vries equation with variable coefficients and perturbing terms in detail based on the general form of the Darboux transformations for some nonlinear evolution equations solvable by the Ablowitz-Kaup-Newell-Segur inverse scattering method. We use this method to generate families of two-soliton solutions and two-periodic solutions.