| Integrability and Solutions of the(2+1)-dimensional Hunter–Saxton Equation |
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| 基金项目： | Supported by National Natural Science Foundation of China under Grant No. 11471174 and NSF of Ningbo under Grant No. 2014A610018 |
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| 摘 要： | 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.
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| 收稿时间： | 2105-11-23 |
Integrability and Solutions of the (2+1)-dimensional Hunter-Saxton Equation |
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| Authors: | Hong-Liu Cai Chang-Zheng Qu |
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| Institution: | Center for Nonlinear Studies, Ningbo University, Ningbo 315211, China |
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| 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. |
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| Keywords: | Hunter-Saxton equation singular solution μ-Hunter-Saxton equation peaked traveling wave solution |
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