EXTENTED PAINLEV? EXPANSION AND NONSTANDARD TRUNCATION SOLUTIONS OF THE KdV EQUATION

LOU SEN-YUE

doi:10.7498/aps.47.1937

Abstract
In this paper,by means of the arbitrariness of the singularity,we have established a new approach of the Painlevé analysis developed by Weiss,Tabor and Carnevale,which is one of the powerful method to study the nonlinear partial differential equations.Selecting some different expansion functions and nonstandard truncations for the KdV equation,we obtained many exact solutions expressed by some complicated implicit functions.
Authors and contacts
LOU SEN-YUE

1.
宁波大学数学物理研究所,宁波 315211
References

Cited By

[1]	Cheng Xue-Ping, Li Jin-Yu, Xue Jiang-Rong. Coupled KdV equation: similarity reduction and analytical solution. Acta Physica Sinica, 2011, 60(11): 110204. doi: 10.7498/aps.60.110204
[2]	Yang Pei, Chen Yong, Li Zhi-Bin. Analytic approximation for the soliton solution of the discrete modified KdV equation. Acta Physica Sinica, 2010, 59(6): 3668-3673. doi: 10.7498/aps.59.3668
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[4]	Liang Li-Wei, Li Xing-Dong, Li Yu-Xia. The extended F-expansion method and new exact solutions of the generalized KdV equation. Acta Physica Sinica, 2009, 58(4): 2159-2163. doi: 10.7498/aps.58.2159
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[8]	Pan Jun-Ting, Gong Lun-Xun. Jacobi elliptic function solutions to the coupled KdV-mKdV equation. Acta Physica Sinica, 2007, 56(10): 5585-5590. doi: 10.7498/aps.56.5585
[9]	Wei Cai-Min, Xia Zun-Quan, Tian Nai-Shuo. New exact soliton-like solution for a generalized stochastic KdV equation. Acta Physica Sinica, 2005, 54(6): 2463-2467. doi: 10.7498/aps.54.2463
[10]	Shi Yu-ren, Lü Ke-Pu, Duan Wen-Shan, Hong Xue-Ren, Zhao Jin-Bao, Yang Hong-Juan. Explicit and exact solutions of the combined KdV equation. Acta Physica Sinica, 2003, 52(2): 267-270. doi: 10.7498/aps.52.267
[11]	LI ZHI-BIN, PAN SU-QI. EXACT SOLITARY WAVE AND SOLITON SOLUTIONS OF THE GENERALIZED FIFTH ORDER KdV EQUATION. Acta Physica Sinica, 2001, 50(3): 402-405. doi: 10.7498/aps.50.402
[12]	Lü KE-PU, SHI YU-REN, DUAN WEN-SHAN, ZHAO JIN-BAO. THE SOLITARY WAVE SOLUTIONS TO KdV-BURGERS EQUATION. Acta Physica Sinica, 2001, 50(11): 2073-2076. doi: 10.7498/aps.50.2073
[13]	ZHANG JIE-FANG, CHEN FANG-YUE. TRUNCATED EXPANSION METHOD AND NEW EXACT SOLITON-LIKE SOLUTION OF THE GENERAL VARIABLE COEFFICIENT KdV EQUATION. Acta Physica Sinica, 2001, 50(9): 1648-1650. doi: 10.7498/aps.50.1648
[14]	ZHU ZUO-NONG. STABILITY OF SOLITARY WAVE FOR THE KdV TYPE EQUATIONAND TRAVELLING WAVE FOR THE KdV-BURGERS TYPE EQUATION. Acta Physica Sinica, 1996, 45(7): 1087-1090. doi: 10.7498/aps.45.1087
[15]	HAI WEN-HUA, XIAO YI. SOLITON SOLUTIONS OF PERIURBED BURGERS-KdV EQUATION. Acta Physica Sinica, 1996, 45(4): 587-594. doi: 10.7498/aps.45.587
[16]	MA WEN-XIU, ZHOU DE-TANG. ON SOLITARY WARE SOLUTIONS TO A GENERALIZED KdV EQNATION. Acta Physica Sinica, 1993, 42(11): 1731-1734. doi: 10.7498/aps.42.1731
[17]	ZHU ZUO-NONG. SOLITON-LIKE SOLUTIONS OF GENERALIZED KdV EQUA-TION WITH EXTERNAL FORCE TERM. Acta Physica Sinica, 1992, 41(10): 1561-1566. doi: 10.7498/aps.41.1561
[18]	ZHU ZUO-NONG. THE SOLITON SOLUTIONS OF GENERALIZED KdV EQUATION. Acta Physica Sinica, 1992, 41(7): 1057-1062. doi: 10.7498/aps.41.1057
[19]	LOU SEN-YUE. THE SOLITON SOLUTIONS OF KdV EQUATION RUNNING TO THE LEFT AND THEIR INTERACTIONS. Acta Physica Sinica, 1991, 40(1): 8-13. doi: 10.7498/aps.40.8
[20]	CHEN DE-FANG, LOU SEN-YUE. DEFORMATION THEORY AMONG TRAVELLING WAVE SOLUTIONS OF KdV EQUATION AND HIGH ORDER KdV EQUATIONS. Acta Physica Sinica, 1991, 40(4): 513-521. doi: 10.7498/aps.40.513

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Vol. 47, Issue 12 - 1998-06-20

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EXTENTED PAINLEV? EXPANSION AND NONSTANDARD TRUNCATION SOLUTIONS OF THE KdV EQUATION

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EXTENTED PAINLEV? EXPANSION AND NONSTANDARD TRUNCATION SOLUTIONS OF THE KdV EQUATION

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