Communications in Theoretical Physics ›› 2022, Vol. 74 ›› Issue (7): 075006. doi: 10.1088/1572-9494/ac729a

• Mathematical Physics • Previous Articles     Next Articles

Conservation laws of the complex short pulse equation and coupled complex short pulse equations

Lihua Zhang,(), Bo Shen, Shuxin Han, Gangwei Wang, Lingshu Wang   

  1. School of Mathematics and Statistics, Hebei University of Economics and Business, Shijiazhuang 050061, China
  • Received: 2022-01-15 Revised: 2022-04-02 Accepted: 2022-05-24 Published: 2022-07-01
  • Contact: Lihua Zhang E-mail:zzlh100@163.com
  • About author: First author contact:Author to whom any correspondence should be addressed.

Abstract:

In this paper, the complex short pulse equation and the coupled complex short pulse equations that can describe the ultra-short pulse propagation in optical fibers are investigated. The two complex nonlinear models are turned into multi-component real models by proper transformations. Lie symmetries are obtained via the classical Lie group method, and the results for the coupled complex short pulse equations contain the existing results as particular cases. Based on the linearizing operator and adjoint linearizing operator for the two real systems, adjoint symmetries can be obtained. Explicit conservation laws are constructed using the symmetry/adjoint symmetry pair (SA) method. Relationships between the nonlinear self-adjointness method and the SA method are investigated.

Key words: complex short pulse equation, coupled complex short pulse equations, symmetries, adjoint symmetries, conservation laws, SA method