A novel method for finding new multi-soliton wave solutions of the completely integrable equations

This paper presents a novel simplest equation method (SEM) to construct multi-soliton wave solutions. The paper proceeds step-by-step with increasing detail about derivation process, first illustrating the algorithm of the SEM and then exploiting an even deeper connection between Burgers' equation and multi-soliton solutions and the simplest equation. Comparing with the Hirota's method, our method provides the possibility for constructing multi-soliton solutions of the completely integrable equations with variable coefficients concisely. Applying such a method to the Gardner equation and the Whitham-Broer-Kaup (WBK) shallow water model, new general forms of multi-soliton solutions are obtained.