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The traditional method of factorization can be used to obtain only theparticular solutions of the Li\'enard type ordinary differential equations. Wesuggest a modification of the approach that can be used to construct generalsolutions . We first demonstrate the effectiveness of our method by dealingwith a solvable form of the modified Emden-type equation and subsequentlyemploy it to obtain the solitary wave solutions of the KdV, mKdV, Rosenau-Hyman(RH) and NLS equations. The solution of the mKdV equation, via the so-calledMuira transform, leads to a singular solution of the KdV equation in additionto the well-known soliton solution supported by it. We obtain the solution ofthe non-integrable RH equation in terms of the Jacobi function and show that,although robust, it is structurally different from the KdV soliton. We alsofind the soliton solution of the NLS equation that accounts for the evolutionof complex envelopes in an optical medium.

Factorization method for nonlinear evolution equations Factorization method for nonlinear evolution equations