EXACT SOLUTIONS OF A CLASS OF UNIQUE-NONLINEAR EVOLUTION EQUATIONS

摘要

In this study, we introduce a modified approach of the factorization method to obtain the particular solutions of the Lienard type ordinary differential equations and eventually employ it to obtain the solitary wave solutions of the Korteweg-de Vries (KdV), modified Korteweg-de Vries (mKdV), Rosenau-Hyman (RH) and Nonlinear Schroedinger (NLS) equations. We obtain the solution of the non-integrable RH equation in terms of the Jacobi sn(u, m) function and show that, although robust, it is structurally different from the KdV soliton. We also find the soliton solution of the NLS equation that accounts for the evolution of complex envelopes in an optical medium.