Variational methods for breather solutions of nonlinear wave equations

被引：5

作者：

Mandel, Rainer ^{[1
]}

Scheider, Dominic ^{[1
]}

机构：

[1] Karlsruhe Inst Technol, Inst Anal, Englerstr 2, D-76131 Karlsruhe, Germany

来源：

NONLINEARITY | 2021年 / 34卷 / 06期

关键词：

breather; nonlinear wave equations; variational methods; HELMHOLTZ; STABILITY;

D O I：

10.1088/1361-6544/abed38

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

We construct infinitely many real-valued, time-periodic breather solutions of the nonlinear wave equation partial derivative U-tt-Delta U=Q(x)|U|Up-2 on T x R-N N >= 2, p > 2 and localized nonnegative Q. These solutions are obtained from critical points of a dual functional and they are weakly localized in space. Our abstract framework allows to find similar existence results for the nonlinear Klein-Gordon equation and biharmonic wave equations.

引用

页码：3618 / 3640

页数：23

共 50 条

[1] Bifurcations of traveling wave and breather solutions of a general class of nonlinear wave equations
Li, JB
Chen, GR
[J]. INTERNATIONAL JOURNAL OF BIFURCATION AND CHAOS, 2005, 15 (09): : 2913 - 2926
[2] Breather and rogue wave solutions of coupled derivative nonlinear Schrodinger equations
Xiang, Xiao-Shuo
Zuo, Da-Wei
[J]. NONLINEAR DYNAMICS, 2022, 107 (01) : 1195 - 1204
[3] Hybrid rogue wave and breather solutions for the nonlinear coupled dispersionless evolution equations
Dong, Hao-Nan
Zhaqilao
[J]. WAVE MOTION, 2024, 125
[4] Breather and rogue wave solutions of coupled derivative nonlinear Schrödinger equations
Xiao-Shuo Xiang
Da-Wei Zuo
[J]. Nonlinear Dynamics, 2022, 107 : 1195 - 1204
[5] BREATHER SOLUTIONS OF THE NONLINEAR-WAVE EQUATION
KICHENASSAMY, S
[J]. COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS, 1991, 44 (07) : 789 - 818
[6] Solitary wave solutions to some classes of nonlinear evolution type equations using inverse variational methods
Kara, A. H.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2007, 67 (11) : 3194 - 3198
[7] Travelling wave and similarity solutions to nonlinear evolution type equations through inverse variational and symmetry methods
Ahmad, Ferhana
Asghar, S.
Kara, A. H.
[J]. NONLINEAR ANALYSIS-THEORY METHODS & APPLICATIONS, 2008, 69 (07) : 2223 - 2229
[8] GLOBAL SOLUTIONS TO NONLINEAR WAVE EQUATIONS ARISING FROM A VARIATIONAL PRINCIPLE
Zeng, Ying
Hu, Yanbo
[J]. JOURNAL OF NONLINEAR AND VARIATIONAL ANALYSIS, 2024, 8 (01): : 1 - 21
[9] On the characterization of breather and rogue wave solutions and modulation instability of a coupled generalized nonlinear Schrodinger equations
Priya, N. Vishnu
Senthilvelan, M.
[J]. WAVE MOTION, 2015, 54 : 125 - 133
[10] Breather solutions of the discrete nonlinear Schrodinger equations with unbounded potentials
Zhang, Guoping
[J]. JOURNAL OF MATHEMATICAL PHYSICS, 2009, 50 (01)

← 1 2 3 4 5 →