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

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...

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Bibliographic Details
Published in:Communications in theoretical physics 2016-04, Vol.65 (4), p.397-404
Main Authors: Cai, Hong-Liu, Qu, Chang-Zheng
Format: Article
Language:English
Subjects:
Corners
Mathematical analysis
Theoretical physics
Transformations
Traveling waves
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Summary: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 mu -Hunter-Saxton equation is presented, and its exact peaked traveling wave solutions are derived.
ISSN:0253-6102
1572-9494
DOI:10.1088/0253-6102/65/4/397