Periodic solutions of nonlinear equations obtained by linear superposition

被引：30

作者：

Cooper, F ^{[1
]}

Khare, A

Sukhatme, U

机构：

[1] Los Alamos Natl Lab, Div Theoret, Los Alamos, NM 87545 USA

[2] Univ Illinois, Dept Phys, Chicago, IL 60607 USA

[3] Inst Phys, Bhubaneswar 751005, Orissa, India

来源：

JOURNAL OF PHYSICS A-MATHEMATICAL AND GENERAL | 2002年 / 35卷 / 47期

关键词：

D O I：

10.1088/0305-4470/35/47/309

中图分类号：

O4 [物理学];

学科分类号：

0702 ;

摘要：

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach we find periodic solutions of the Kadomtsev-Petviashvili equation, the nonlinear Schrodinger equation, the lambdaphi(4) model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known-periodic solutions. This unusual procedure for generating solutions of nonlinear differential equations is successful as a consequence of. some powerful, recently discovered, cyclic identities satisfied by the Jacobi elliptic functions.

引用

页码：10085 / 10100

页数：16

共 27 条

[11] EXACT N-SOLITON SOLUTIONS OF WAVE-EQUATION OF LONG WAVES IN SHALLOW-WATER AND IN NONLINEAR LATTICES [J].

HIROTA, R .

JOURNAL OF MATHEMATICAL PHYSICS, 1973, 14 (07) :810-814

[12] Linear superposition in nonlinear equations [J].

Khare, A ;

Sukhatme, U .

PHYSICAL REVIEW LETTERS, 2002, 88 (24) :4-244101

[13] Cyclic identities involving Jacobi elliptic functions [J].

Khare, A ;

Sukhatme, U .

JOURNAL OF MATHEMATICAL PHYSICS, 2002, 43 (07) :3798-3806

[14]

KHARE A, 2002, MATHPH020719

[15]

KHARE A, 2002, MATHPH0204054

[16] Jacobi elliptic function expansion method and periodic wave solutions of nonlinear wave equations [J].

Liu, SK ;

Fu, ZT ;

Liu, SD ;

Zhao, Q .

PHYSICS LETTERS A, 2001, 289 (1-2) :69-74

[17]

MANEUF S, 1988, OPT COMMUN, V66, P325, DOI 10.1016/0030-4018(88)90424-5

[18] EXPERIMENTAL-OBSERVATION OF PICOSECOND PULSE NARROWING AND SOLITONS IN OPTICAL FIBERS [J].

MOLLENAUER, LF ;

STOLEN, RH ;

GORDON, JP .

PHYSICAL REVIEW LETTERS, 1980, 45 (13) :1095-1098

[19]

NEWELL AC, 1985, SOLITONS MATH PHYSIC

[20] EXACT TRAVELING WAVE SOLUTIONS OF A CLASS OF NONLINEAR DIFFUSION-EQUATIONS BY REDUCTION TO A QUADRATURE [J].

OTWINOWSKI, M ;

PAUL, R ;

LAIDLAW, WG .

PHYSICS LETTERS A, 1988, 128 (09) :483-487

← 1 2 3 →