Stability of Solitary Waves for a Generalized Higher-Order Shallow Water Equation

被引:2
作者
Dundar, Nurhan [1 ]
Polat, Necat [1 ]
机构
[1] Dicle Univ, Dept Math, TR-21280 Diyarbakir, Turkey
关键词
Shallow water equation; Solitary waves; Variational methods; Stability; CONCENTRATION-COMPACTNESS PRINCIPLE; CAUCHY-PROBLEM; STANDING WAVES; WELL-POSEDNESS; CALCULUS;
D O I
10.2298/FIL1405007D
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
In this work, we consider solitary wave solutions of a generalized higher-order shallow water equation. We investigate the existence and stability of solitary waves of the equation.
引用
收藏
页码:1007 / 1017
页数:11
相关论文
共 20 条
[1]  
[Anonymous], CONT MATH
[2]   ORBITAL STABILITY OF STANDING WAVES FOR SOME NON-LINEAR SCHRODING EQUATIONS [J].
CAZENAVE, T ;
LIONS, PL .
COMMUNICATIONS IN MATHEMATICAL PHYSICS, 1982, 85 (04) :549-561
[3]  
DULLIN H, 2001, PHYS REV LETT, V87, P1945
[4]  
Dundar N., LOCAL WELL POS UNPUB
[5]   Blow-up phenomena and stability of solitary waves for a generalized Dullin-Gottwald-Holm equation [J].
Dundar, Nurhan ;
Polat, Necat .
BOUNDARY VALUE PROBLEMS, 2013,
[6]   STABILITY THEORY OF SOLITARY WAVES IN THE PRESENCE OF SYMMETRY .1. [J].
GRILLAKIS, M ;
SHATAH, J ;
STRAUSS, W .
JOURNAL OF FUNCTIONAL ANALYSIS, 1987, 74 (01) :160-197
[7]   ON THE DERIVATIVE NONLINEAR SCHRODINGER-EQUATION [J].
HAYASHI, N ;
OZAWA, T .
PHYSICA D, 1992, 55 (1-2) :14-36
[8]   Well-posedness of the Cauchy problem for a shallow water equation on the circle [J].
Himonas, AA ;
Misiolek, C .
JOURNAL OF DIFFERENTIAL EQUATIONS, 2000, 161 (02) :479-495
[9]   A stability analysis of fifth-order water wave models [J].
Levandosky, SP .
PHYSICA D, 1999, 125 (3-4) :222-240
[10]   Stability of solitary waves of a generalized Ostrovsky equation [J].
Levandosky, Steve ;
Liu, Yue .
SIAM JOURNAL ON MATHEMATICAL ANALYSIS, 2006, 38 (03) :985-1011