Existence of periodic travelling-wave solutions of nonlinear, dispersive wave equations

被引：20

作者：

Chen, HQ ^{[1
]}

机构：

[1] Univ Memphis, Dept Math Sci, Memphis, TN 38152 USA

[2] Univ Illinois, Dept Math Stat & Comp Sci, Chicago, IL 60607 USA

来源：

NONLINEARITY | 2004年 / 17卷 / 06期

关键词：

D O I：

10.1088/0951-7715/17/6/003

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

For general classes of nonlinear, dispersive wave equations, we discuss the existence of the analogue of the cnoidal-wave solutions of the Korteweg-de Vries equation. The solutions in question have travelling and periodic features. The topological-degree theory of positive operators on Banach spaces is applied.

引用

页码：2041 / 2056

页数：16

共 50 条

[1] EXISTENCE AND COMPUTATION OF PERIODIC TRAVELLING-WAVE SOLUTIONS OF A DISPERSIVE SYSTEM
Munoz Grajales, Juan Carlos
COMMUNICATIONS IN MATHEMATICAL SCIENCES, 2012, 10 (03) : 917 - 944
[2] Classification of all travelling-wave solutions for some nonlinear dispersive equations
Lenells, Jonatan
PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2007, 365 (1858): : 2291 - 2298
[3] Periodic travelling wave solutions of nonlinear wave equations
Shi, YM
Li, TT
Qin, TH
NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 1999, 35 (07) : 917 - 923
[4] Travelling-wave solutions of coupled nonlinear evolution equations
Malfliet, W
MATHEMATICS AND COMPUTERS IN SIMULATION, 2003, 62 (1-2) : 101 - 108
[5] Existence and stability of periodic travelling-wave solutions of the Benjamin equation
Samaniego, BA
Pava, JA
COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 2005, 4 (02) : 367 - 388
[6] A numerical scheme for periodic travelling-wave simulations in some nonlinear dispersive wave models
Alvarez, J.
Duran, A.
JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2011, 235 (07) : 1790 - 1797
[7] Travelling and periodic wave solutions of some nonlinear wave equations
Khater, AH
Hassan, AA
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2004, 59 (7-8): : 389 - 396
[8] GLOBAL EXISTENCE OF SOLUTIONS TO NONLINEAR DISPERSIVE WAVE EQUATIONS
Hayashi, Nakao
Kobayashi, Seishru
Naumkin, Pavel I.
DIFFERENTIAL AND INTEGRAL EQUATIONS, 2012, 25 (7-8) : 685 - 698
[9] TRAVELLING-WAVE SOLUTIONS OF NERVE IMPULSE EQUATIONS
CARPENTER, GA
NOTICES OF THE AMERICAN MATHEMATICAL SOCIETY, 1975, 22 (01): : A19 - A19
[10] Travelling-Wave Solutions for Wave Equations with Two Exponential Nonlinearities
Mancas, Stefan C.
Rosu, Haret C.
Perez-Maldonado, Maximino
ZEITSCHRIFT FUR NATURFORSCHUNG SECTION A-A JOURNAL OF PHYSICAL SCIENCES, 2018, 73 (10): : 883 - 892

← 1 2 3 4 5 →