Orbital Stability and Instability of Solitary Waves for a Class of Dispersive Symmetric Regularized Long-Wave Equation

被引：0
作者：
Sevdzhan Hakkaev
机构：
[1] Istanbul Aydin University,Department of Mathematics and Computer Science
来源：
Mediterranean Journal of Mathematics | 2019年 / 16卷
关键词：
Solitary waves; regularized long-wave equation; orbital stability; 35B35; 35B40; 35G30;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
This paper studies the orbital stability and instability of solitary wave solutions of the generalized symmetric regularized long-wave-type equations. It is shown that a traveling wave may be stable or unstable depending on the range of the waves speed of propagation and the relation between the dispersion (i.e., the order of the pseudodifferential operator) and the nonlinearity.
引用
收藏
相关论文
共 28 条
[1]  
Albert JP(1992)Positivity properties and stability of solitary wave solutions of model equations for long waves Commun. Partial Differ. Equ. 17 1-22
[2]  
Albert JP(1991)Total positivity and stability of internal waves in stratified fluids of finite depth IMA J. Appl. Math. 46 1-19
[3]  
Bona JL(1987)Suffucient conditions for stability of solitary-wave solutions of model equations for long waves Physica 24D 343-366
[4]  
Albert JP(1972)The stability of solitary waves Proc. R. Soc. Lond. Ser. A 328 153-183
[5]  
Bona JL(1990)Solitary-Wave Solutions of Nonlinear Problems Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 331 195-244
[6]  
Henry DB(1975)On the stability theory of solitary waves Proc. R. Soc. Lond. Ser. A 344 363-374
[7]  
Benjamin TB(1987)Stability and instability of solitary waves of Korteweg-de Vries type Proc. R. Soc. Lond. Ser. A 411 395-412
[8]  
Benjamin T. B.(1988)Global existence of smooth solutions and stability of solitary waves for generalized Boussinesq equation Commun. Math. Phys. 118 1529-68
[9]  
Bona J. L.(1998)Stability and instability of solitary waves for generalized symmetric-regularized-long-wave equations Physica D 118 53-197
[10]  
Bose D. K.(1987)Stability theory of solitary waves in the presence of symmetry I J. Funct. Anal. 74 160-348
123