Symmetries and conservation laws of the Yao–Zeng two-component short-pulse equation

Abstract

Abstract This paper uses the Lie group method to analyze the symmetries of the Yao–Zeng two-component short-pulse equation which describes the propagation of polarized ultrashort light pulses in cubically nonlinear anisotropic optical fibers. Similarity reductions and exact solutions are obtained by constructing an optimal system of one-dimensional subalgebras. Moreover, the explicit solutions are constructed by the power series method and the convergence of power series solutions is proved. In addition, nonlinear self-adjointness and conservation laws of this system are discussed.

Keywords

• The Yao–Zeng two-component short-pulse equation
• Symmetries
• The power series solutions
• Conservation laws