Communications in Theoretical Physics ›› 2016, Vol. 65 ›› Issue (04): 397-404.

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Integrability and Solutions of the (2+1)-dimensional Hunter-Saxton Equation

Hong-Liu Cai, Chang-Zheng Qu   

  1. Center for Nonlinear Studies, Ningbo University, Ningbo 315211, China
  • Received: 2105-11-23 Revised: 2015-12-29 Published: 2016-04-01
  • Funding Information: 

    Supported by National Natural Science Foundation of China under Grant No. 11471174 and NSF of Ningbo under Grant No. 2014A610018

Abstract: In this paper, the (2+1)-dimensional Hunter-Saxton equation is proposed and studied. It is shown that the (2+1)-dimensional Hunter-Saxton equation can be transformed to the Calogero-Bogoyavlenskii-Schiff equation by reciprocal transformations. Based on the Lax-pair of the Calogero-Bogoyavlenskii-Schiff equation, a non-isospectral Lax-pair of the (2+1)-dimensional Hunter-Saxton equation is derived. In addition, exact singular solutions with a finite number of corners are obtained. Furthermore, the (2+1)-dimensional μ-Hunter-Saxton equation is presented, and its exact peaked traveling wave solutions are derived.

Key words: Hunter-Saxton equation, singular solution, μ-Hunter-Saxton equation, peaked traveling wave solution

PACS numbers: 

  • 02.30.Ik