Explicit Exact Solitary Wave Solutions for the Kundu Equation and the Derivative Schrödinger Equation

Abstract

Studying explicit exact solutions of nonlinear evolution equations is a vastly open research field. In this paper, we are giving a new approach called the algebraic curve method to the study of the Kundu equation and the derivative Schrödinger equation. Using this technique we obtain the explicit exact solitary solutions for the Kundu equation and two new explicit exact solitary solutions for the derivative Schrödinger equation, which are different from the previous ones. Applications of this technique to some other nonlinear evolution equations are also presented.