Orbital stability of periodic traveling-wave solutions for the log-KdV equation

被引：9
|
作者：
Natali, Fabio [1 ]
Pastor, Ademir [2 ]
Cristofani, Fabricio [1 ]
机构：
[1] Univ Estadual Maringa, Dept Matemat, Ave Colombo 5790, BR-87020900 Maringa, Parana, Brazil
[2] IMECC UNICAMP, Rua Sergio Buarque de Holanda 651, BR-13083859 Campinas, SP, Brazil
来源：
JOURNAL OF DIFFERENTIAL EQUATIONS | 2017年 / 263卷 / 05期
基金：
巴西圣保罗研究基金会;
关键词：
Orbital stability; Log-KdV equation; Periodic waves; SOLITARY WAVES;
D O I：
10.1016/j.jde.2017.04.004
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper we establish the orbital stability of periodic waves related to the logarithmic Korteweg-de Vries equation. Our motivation is inspired in the recent work [3], in which the authors established the well-posedness and the linear stability of Gaussian solitary waves. By using the approach put forward recently in [20] to construct a smooth branch of periodic waves as well as to get the spectral properties of the associated linearized operator, we apply the abstract theories in [13] and [25] to deduce the orbital stability of the periodic traveling waves in the energy space. (C) 2017 Elsevier Inc. All rights reserved.
引用
收藏
页码：2630 / 2660
页数：31
相关论文
共 50 条
  • [31] EXISTENCE AND ORBITAL STABILITY OF PERIODIC WAVE SOLUTIONS FOR THE NONLINEAR SCHRoDINGER EQUATION
    Chen, Aiyong
    Wen, Shuangquan
    Huang, Wentao
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2012, 2 (02): : 137 - 148
  • [32] Periodic traveling-wave solution of the Sakuma-Nishiguchi equation
    Rowland, DR
    Jovanoski, Z
    PHYSICAL REVIEW B, 1996, 54 (19): : 13484 - 13486
  • [33] ORBITAL STABILITY OF PERIODIC TRAVELING WAVE SOLUTIONS TO THE GENERALIZED LONG-SHORT WAVE EQUATIONS
    Zheng, Xiaoxiao
    Xin, Jie
    Peng, Xiaoming
    JOURNAL OF APPLIED ANALYSIS AND COMPUTATION, 2019, 9 (06): : 2389 - 2408
  • [34] ON PERIODIC TRAVELING WAVE SOLUTIONS OF BOUSSINESQ EQUATION
    LIU, BP
    PAO, CV
    QUARTERLY OF APPLIED MATHEMATICS, 1984, 42 (03) : 311 - 319
  • [35] Existence Analysis of Traveling Wave Solutions for a Generalization of KdV Equation
    Long, Yao
    Chen, Can
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2013, 2013
  • [36] PERIODIC TRAVELING-WAVE SOLUTIONS OF NONLINEAR DISPERSIVE EVOLUTION EQUATIONS
    Chen, Hongqiu
    Bona, Jerry L.
    DISCRETE AND CONTINUOUS DYNAMICAL SYSTEMS, 2013, 33 (11-12) : 4841 - 4873
  • [37] New solitary wave solutions and periodic wave solutions for the compound KdV equation
    Zhang, Weiguo
    Li, Shaowei
    Zhang, Lu
    Ning, Tongke
    CHAOS SOLITONS & FRACTALS, 2009, 39 (01) : 143 - 149
  • [38] Nonlinear Stability of Periodic Traveling-Wave Solutions of Viscous Conservation Laws in Dimensions One and Two
    Johnson, Mathew A.
    Zumbrun, Kevin
    SIAM JOURNAL ON APPLIED DYNAMICAL SYSTEMS, 2011, 10 (01): : 189 - 211
  • [39] More Exact Traveling Wave Solutions for Compound KdV Equation and MKdV Equation
    Cao, DongBo
    Pan, LiuXian
    Yan, JiaRen
    MATERIALS SCIENCE AND INFORMATION TECHNOLOGY, PTS 1-8, 2012, 433-440 : 3642 - +
  • [40] On traveling wave solutions to combined KdV-mKdV equation and modified Burgers-KdV equation
    Bekir, Ahmet
    COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2009, 14 (04) : 1038 - 1042
12345