First integrals, solutions and conservation laws of the derivative nonlinear Schrödinger equation

Abstract

We study the derivative nonlinear Schrödinger equation which has several applications, such as the propagation of circular polarized nonlinear Alfvén waves in plasmas. We present general and special solutions of this equation using first integrals. Classical Lie group theory along with power series method is also applied to obtain exact analytical solutions of this equation. Finally, conservation laws of the underlying equation are constructed through the use of the multiplier method.

Keywords

• First integrals
• Derivative nonlinear Schrödinger equation
• Lie point symmetries
• Power series
• Exact analytical solutions
• Conservation laws