Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

doi:10.1088/1674-1056/27/4/040202

中国物理B ›› 2018, Vol. 27 ›› Issue (4): 40202-040202.doi: 10.1088/1674-1056/27/4/040202

Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

Han-Ze Liu(刘汉泽), Li-Xiang Zhang(张丽香)

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

收稿日期:2017-12-01 修回日期:2018-01-01 出版日期:2018-04-05 发布日期:2018-04-05
通讯作者: Han-Ze Liu E-mail:bzliuhanze@163.com
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11171041) and the High-Level Personnel Foundation of Liaocheng University (Grant No. 31805).

Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

Han-Ze Liu(刘汉泽), Li-Xiang Zhang(张丽香)

School of Mathematical Sciences, Liaocheng University, Liaocheng 252059, China

Received:2017-12-01 Revised:2018-01-01 Online:2018-04-05 Published:2018-04-05
Contact: Han-Ze Liu E-mail:bzliuhanze@163.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11171041) and the High-Level Personnel Foundation of Liaocheng University (Grant No. 31805).

摘要/Abstract

摘要： This paper is concerned with the generalized variable-coefficient nonlinear evolution equation (vc-NLEE). The complete integrability classification is presented, and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis. Then, the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method, and the Lax pairs (LP) of the vc-NLEEs are constructed in terms of the integrable conditions.

关键词: Painlevé test, integrability classification, Lax pair, truncated expansion, exact solution

Abstract: This paper is concerned with the generalized variable-coefficient nonlinear evolution equation (vc-NLEE). The complete integrability classification is presented, and the integrable conditions for the generalized variable-coefficient equations are obtained by the Painlevé analysis. Then, the exact explicit solutions to these vc-NLEEs are investigated by the truncated expansion method, and the Lax pairs (LP) of the vc-NLEEs are constructed in terms of the integrable conditions.

Key words: Painlevé test, integrability classification, Lax pair, truncated expansion, exact solution

中图分类号: (Partial differential equations)

02.30.Jr

02.30.Ik (Integrable systems)

刘汉泽, 张丽香. Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation[J]. 中国物理B, 2018, 27(4): 40202-040202.

Han-Ze Liu(刘汉泽), Li-Xiang Zhang(张丽香). Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation[J]. Chin. Phys. B, 2018, 27(4): 40202-040202.

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Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

Integrability classification and exact solutions to generalized variable-coefficient nonlinear evolution equation

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