The extended auxiliary equation method for the KdV equation with variable coefficients

doi:10.1088/1674-1056/20/10/100507

中国物理B ›› 2011, Vol. 20 ›› Issue (10): 100507-100507.doi: 10.1088/1674-1056/20/10/100507

The extended auxiliary equation method for the KdV equation with variable coefficients

周先春¹, 陈才生², 石兰芳³

(1)College of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China; (2)College of Mathematics, Hohai University, Nanjing 210098, China; (3)College of Mathematics, Hohai University, Nanjing 210098, China; College of Mathematics and Physics, Nanjing University of Information Science and Technology, Nanjing 210044, China

收稿日期:2010-12-29 修回日期:2011-04-08 出版日期:2011-10-15 发布日期:2011-10-15
基金资助:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010B17914) and the National Natural Science Foundation of China (Grant No. 10926162).

The extended auxiliary equation method for the KdV equation with variable coefficients

Shi Lan-Fang(石兰芳)^a)b)^†, Chen Cai-Sheng(陈才生)^a), and Zhou Xian-Chun(周先春)^c)

^a College of Mathematics, Hohai University, Nanjing 210098, China; ^b College of Mathematics, Hohai University, Nanjing 210098, China; ^c College of Electronic and Information Engineering, Nanjing University of Information Science and Technology, Nanjing 210044, China

Received:2010-12-29 Revised:2011-04-08 Online:2011-10-15 Published:2011-10-15
Supported by:
Project supported by the Fundamental Research Funds for the Central Universities (Grant No. 2010B17914) and the National Natural Science Foundation of China (Grant No. 10926162).

摘要/Abstract

摘要： This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.

关键词: extended auxiliary equation method, KdV equation with variable coefficients, exact solutions

Abstract: This paper applies an extended auxiliary equation method to obtain exact solutions of the KdV equation with variable coefficients. As a result, solitary wave solutions, trigonometric function solutions, rational function solutions, Jacobi elliptic doubly periodic wave solutions, and nonsymmetrical kink solution are obtained. It is shown that the extended auxiliary equation method, with the help of a computer symbolic computation system, is reliable and effective in finding exact solutions of variable coefficient nonlinear evolution equations in mathematical physics.

Key words: extended auxiliary equation method, KdV equation with variable coefficients, exact solutions

中图分类号: (Solitons)

05.45.Yv

02.60.Cb (Numerical simulation; solution of equations) 02.30.Jr (Partial differential equations)

石兰芳, 陈才生, 周先春. The extended auxiliary equation method for the KdV equation with variable coefficients[J]. 中国物理B, 2011, 20(10): 100507-100507.

Shi Lan-Fang(石兰芳), Chen Cai-Sheng(陈才生), and Zhou Xian-Chun(周先春) . The extended auxiliary equation method for the KdV equation with variable coefficients[J]. Chin. Phys. B, 2011, 20(10): 100507-100507.

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The extended auxiliary equation method for the KdV equation with variable coefficients

The extended auxiliary equation method for the KdV equation with variable coefficients

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