Approximate solutions of nonlinear PDEs by the invariant expansion

doi:10.1088/1674-1056/21/12/120204

Chin. Phys. B ›› 2012, Vol. 21 ›› Issue (12): 120204-120204.doi: 10.1088/1674-1056/21/12/120204

Approximate solutions of nonlinear PDEs by the invariant expansion

吴江龙^a, 楼森岳^b

a Faculty of Science, Ningbo University, Ningbo 315211, China;
b Center of Nonlinear Science, Ningbo University, Ningbo 315211, China

收稿日期:2012-04-28 修回日期:2012-06-20 出版日期:2012-11-01 发布日期:2012-11-01
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 11175092), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201017148), and K. C. Wong Magna Fund in Ningbo University.

Approximate solutions of nonlinear PDEs by the invariant expansion

Wu Jiang-Long (吴江龙)^a, Lou Sen-Yue (楼森岳)^b

a Faculty of Science, Ningbo University, Ningbo 315211, China;
b Center of Nonlinear Science, Ningbo University, Ningbo 315211, China

Received:2012-04-28 Revised:2012-06-20 Online:2012-11-01 Published:2012-11-01
Contact: Wu Jiang-Long E-mail:wjlazxm@sina.com;375516508@qq.com
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 11175092), Scientific Research Fund of Zhejiang Provincial Education Department (Grant No. Y201017148), and K. C. Wong Magna Fund in Ningbo University.

摘要/Abstract

摘要： It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear system. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as Korteweg-de Vries (KdV) equation with fifth-order dispersion term, perturbed fourth-order KdV equation, KdV-Burgers equation, and Boussinesq type of equation.

关键词: approximate solution, invariant expansion, Mobious transformation invariance

Abstract: It is difficult to obtain exact solutions of the nonlinear partial differential equations (PDEs) due to the complexity and nonlinearity, especially for non-integrable systems. In this paper, some reasonable approximations of real physics are considered, and the invariant expansion is proposed to solve real nonlinear system. A simple invariant expansion with quite a universal pseudopotential is used for some nonlinear PDEs such as Korteweg-de Vries (KdV) equation with fifth-order dispersion term, perturbed fourth-order KdV equation, KdV-Burgers equation, and Boussinesq type of equation.

Key words: approximate solution, invariant expansion, Mobious transformation invariance

中图分类号: (Partial differential equations)

02.30.Jr

47.10.ab (Conservation laws and constitutive relations) 02.30.Ik (Integrable systems)

吴江龙, 楼森岳. Approximate solutions of nonlinear PDEs by the invariant expansion[J]. Chin. Phys. B, 2012, 21(12): 120204-120204.

Wu Jiang-Long (吴江龙), Lou Sen-Yue (楼森岳). Approximate solutions of nonlinear PDEs by the invariant expansion[J]. Chin. Phys. B, 2012, 21(12): 120204-120204.

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Approximate solutions of nonlinear PDEs by the invariant expansion

Approximate solutions of nonlinear PDEs by the invariant expansion

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