NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS

Applied Mathematics and Mechanics (English Edition) ›› 2003, Vol. 24 ›› Issue (11): 1259-1263.

NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS

张解放^1,2, 刘宇陆²

1. Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China;
2. Institute of Shanghai Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

收稿日期:2001-04-19 修回日期:2003-05-20 出版日期:2003-11-18 发布日期:2003-11-18
基金资助:
the Natural Science Foundation of Zhejiang Province of China (100039)

NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS

ZHANG Jie-fang^1,2, LIU Yu-lu ²

1. Institute of Nonlinear Physics, Zhejiang Normal University, Jinhua, Zhejiang 321004, P. R. China;
2. Institute of Shanghai Applied Mathematics and Mechanics, Shanghai University, Shanghai 200072, P. R. China

Received:2001-04-19 Revised:2003-05-20 Online:2003-11-18 Published:2003-11-18
Supported by:
the Natural Science Foundation of Zhejiang Province of China (100039)

摘要/Abstract

摘要： The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.

Abstract: The truncated expansion method for finding explicit and exact soliton-like solution of variable coefficient nonlinear evolution equation was described. The crucial idea of the method was first the assumption that coefficients of the truncated expansion formal solution are functions of time satisfying a set of algebraic equations, and then a set of ordinary different equations of undetermined functions that can be easily integrated were obtained. The simplicity and effectiveness of the method by application to a general variable coefficient KdV-MKdV equation with three arbitrary functions of time is illustrated.

中图分类号:

O175

张解放;刘宇陆. NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(11): 1259-1263.

ZHANG Jie-fang;LIU Yu-lu . NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS[J]. Applied Mathematics and Mechanics (English Edition), 2003, 24(11): 1259-1263.

参考文献

[1] Chen Z X, Guo B Y,Xiang L W. Complete integrability and analytic solutions of a KdV-typeequation[J]. Journal of Mathematical Physics,1990,31(12):2851-2855.
[2] LOU Sen-yue, RUAN Hang-yu. Conservative laws of the variable coefficient KdV and MKdVequation[J]. Acta Physica Sinica,1992,41(2):182-187.(in Chinese)
[3] ZHU Zuo-nong. Solitary wave solution of the generalized KdV with external force term[J]. ActaPhysica Sinica, 1992,41(10): 1561-1565.(in Chinese)
[4] LI Yi-sheng.ZHU Guo-cheng. Symmetries of a variable isospectral evolution equation[J]. ChineseScience Bulletin (Kexue Tonghao),1986,31(19):1449-1453. (in Chinese)
[5] Gazeau J P,Winternitz P. Symmetries of variable coefficient KdV equations[J]. Journal of Mathematical Physics, 1992,33(12):4087-4102.
[6] LOU Sen-yue. Generalized Boussinesq equation and KdV equation-Painleve properties, Backlund transformations and Lax pairs[ J]. Science in Chinese, Ser A, 1991,21(6):622-631.(in Chinese)
[7] ZHU Zuo-nong. On the KdV-type equation with variable coefficients [J]. Journal of Physics A: Mathematical and General,1995,28(19):5673-5684.
[8] RUAN Hang-yu, CHEN Yi-xin. New method of seeking for the exact solution of variable coefficient nonlinear equation[J]. Acta Physica Sinica,2000,49(2):177-180.(in Chinese)
[9] WEN Shuang-chun.XU Wen-cheng,GUO Qi, et al. Evolution of soliton of nonlinear Schordinger equation with variable parameters[J]. Science in Chinese, Ser A,27(10): 949-953. (in Chinese)
[10] XU Bao-zhi,ZHAO Shen-qi. Inverse scattering transformation for the variable coefficient sine-gor-don type equations[J]. Applied Mathematics-JCU, Ser B, 1994,9(3):331-337.
[11] LIU Xi-qiang. Exact solution of the variable coefficient KdV and SG type equations[J]. Applied Mathematics-JCU, Ser B, 1998,13(1): 25-30.
[12] ZHEN Yu-kun,Chan W L. Backlund transformation for the non-isospectral and variable coefficient nonlinear Schordinger equation [J]. Journal of Physics A: Mathematical and General, 1989,22 (5):441-449.
[13] YAN Zhen-ya, ZHANG Hong-qing. Exact solution of variable coefficient KdV-MKdV with three arbitrary functions[J]. Acta Physica Sinica, 1999,48(11):1957-1961.(in Chinese)
[14] ZHANG Jie-fang, CHEN Fang-yue. Truncated expansion method and new soliton-like solution of the general variable coefficient KdV equation[J]. Acta Physica Sinica,2001,50(9):1648-1650.(in Chinese)

[1]	Shujun YOU, Boling GUO. Global solution for quantum Zakharov equations[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(4): 603-616.
[2]	Shan JIANG, Longxiang DAI, Hao CHEN, Hongping HU, Wei JIANG, Xuedong CHEN. Folding beam-type piezoelectric phononic crystal with low-frequency and broad band gap[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 411-422.
[3]	Lihua LIU, Chaolu TEMUER. Symmetry analysis of modified 2D Burgers vortex equation for unsteady case[J]. Applied Mathematics and Mechanics (English Edition), 2017, 38(3): 453-468.
[4]	W. PAULSEN, M. MANNING. Finding vibrations of inclined cable structures by approximately solving governing equations for exterior matrix[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(11): 1383-1402.
[5]	A. K. VASHISHTH, A. DAHIYA, V. GUPTA. Generalized Bleustein-Gulyaev type waves in layered porous piezoceramic structure[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(9): 1223-1242.
[6]	A. M. SIDDIQUI, H. ASHRAF, A. WALAIT, T. HAROON. On study of horizontal thin film flow of Sisko fluid due to surface tension gradient[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(7): 847-862.
[7]	Zhijie SHI, Yuesheng WANG, Chuanzeng ZHANG. Band structure calculations of in-plane waves in two-dimensional phononic crystals based on generalized multipole technique[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(5): 557-580.
[8]	Wancheng SHENG;Ying ZENG. Generalized δ-entropy condition to Riemann solution for Chaplygin gas in traffic flow[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 353-364.
[9]	Yinshan YUN;Chaolu TEMUER. Classical and nonclassical symmetry classifications of nonlinear wave equation with dissipation[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 365-378.
[10]	Chao MIN;Nanjing HUANG;Zhibin LIU;Liehui ZHANG. Existence of solutions for implicit fuzzy differential inclusions[J]. Applied Mathematics and Mechanics (English Edition), 2015, 36(3): 401-416.
[11]	陈学慧;郑连存;张欣欣. MHD flow of power-law fluid on moving surface with power-law velocity and special injection/blowing[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(12): 1555-1564.
[12]	杨曼丽;卢志明;刘宇陆. Self-similar behavior for multicomponent coagulation[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(11): 1353-1360.
[13]	高军;罗纪生. Mode decomposition of nonlinear eigenvalue problems and application in flow stability[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 667-674.
[14]	H. YASMIN;T. HAYAT;A. ALSAEDI;H. H. ALSULAMI. Peristaltic flow of Johnson-Segalman fluid in asymmetric channel with convective boundary condition[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(6): 697-716.
[15]	张燕林平司新辉. Perturbation solutions for asymmetric laminar flow in porous channel with expanding and contracting walls[J]. Applied Mathematics and Mechanics (English Edition), 2014, 35(2): 203-220.

NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS

NEW TRUNCATED EXPANSION METHOD AND SOLITON-LIKE SOLUTION OF VARIABLE COEFFICIENT KdV-MKdV EQUATION WITH THREE ARBITRARY FUNCTIONS

PDF

可视化

摘要/Abstract

引用本文

使用本文

参考文献

相关文章 15

编辑推荐

Metrics

本文评价