Algebraic operator method for the construction of solitary solutions to nonlinear differential equations

被引：20

作者：

Navickas, Zenonas ^{[1
]}

Bikulciene, Liepa ^{[1
]}

Rahula, Maido ^{[2
]}

Ragulskis, Minvydas ^{[3
]}

机构：

[1] Kaunas Univ Technol, Dept Appl Math, LT-51368 Kaunas, Lithuania

[2] Univ Tartu, Inst Pure Math, EE-50409 Tartu, Estonia

[3] Kaunas Univ Technol, Res Grp Math & Numer Anal Dynam Syst, LT-51368 Kaunas, Lithuania

来源：

COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION | 2013年 / 18卷 / 06期

关键词：

KdV equation; Generalized operator of differentiation; Solitary solution; Condition of existence; DE-VRIES EQUATION; TANH-FUNCTION METHOD; WAVE SOLUTIONS; EXP-FUNCTION; EXPANSION METHOD; KDV-TYPE; EVOLUTION;

D O I：

10.1016/j.cnsns.2012.10.009

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

Solutions of the KdV equation are derived by the algebraic operator method based on generalized operators of differentiation. The algebraic operator method based on the generalized operator of differentiation is exploited for the derivation of analytic solutions to the KdV equation. The structure of solitary solutions and explicit conditions of existence of these solutions in the subspace of initial conditions are derived. It is shown that special solitary solutions exist only on a line in the parameter plane of initial and boundary conditions. This new theoretical result may lead to important findings in a variety of practical applications. (C) 2012 Elsevier B. V. All rights reserved.

引用

页码：1374 / 1389

页数：16

共 41 条

[1] Ablowitzand M.A., 1991, SOLITONS NONLINEAR E
[2] RATIONAL AND ELLIPTIC SOLUTIONS OF KORTEWEG DE-VRIES EQUATION AND A RELATED MANY-BODY PROBLEM
AIRAULT, H
MCKEAN, HP
MOSER, J
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1977, 30 (01) : 95 - 148
[3] Chen Yong, 2003, MM RESEARCH PREPRINT, V29, P382
[4] Debath L, 1998, NONLINEAR WATER PART
[5] Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method
Ebaid, A.
[J]. PHYSICS LETTERS A, 2007, 365 (03) : 213 - 219
[6] Extended tanh-function method and its applications to nonlinear equations
Fan, EG
[J]. PHYSICS LETTERS A, 2000, 277 (4-5) : 212 - 218
[7] Explicit soliton asymptotics for the Korteweg-de Vries equation on the half-line
Fokas, A. S.
Lenells, J.
[J]. NONLINEARITY, 2010, 23 (04) : 937 - 976
[8] METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION
GARDNER, CS
GREENE, JM
KRUSKAL, MD
MIURA, RM
[J]. PHYSICAL REVIEW LETTERS, 1967, 19 (19) : 1095 - &
[9] Exp-function method for nonlinear wave equations
He, Ji-Huan
Wu, Xu-Hong
[J]. CHAOS SOLITONS & FRACTALS, 2006, 30 (03) : 700 - 708
[10] EXACT SOLUTION OF KORTEWEG-DE VRIES EQUATION FOR MULTIPLE COLLISIONS OF SOLITONS
HIROTA, R
[J]. PHYSICAL REVIEW LETTERS, 1971, 27 (18) : 1192 - +

← 1 2 3 4 5 →