Geodesic
Stability of solitary wave solutions for equations of short and long dispersive waves
Electronic journal of differential equations, Tome 2006 (2006)
In this paper, we consider the existence and stability of a novel set of solitary-wave solutions for two models of short and long dispersive waves in a two layer fluid. We prove the existence of solitary waves via the Concentration Compactness Method. We then introduce the sets of solitary waves obtained through our analysis for each model and we show that them are stable provided the associated action is strictly convex. We also establish the existence of intervals of convexity for each associated action. Our analysis does not depend of spectral conditions.
Classification : 35Q35, 35Q53, 35Q55, 35B35, 58E30, 76B15
Keywords: dispersive wave equations, variational methods, stability, solitary wave solutions 
@article{EJDE_2006__2006__a111,
     author = {Angulo Pava,  Jaime},
     title = {Stability of solitary wave solutions for equations of short and long dispersive waves},
     journal = {Electronic journal of differential equations},
     year = {2006},
     volume = {2006},
     zbl = {1110.35071},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a111/}
}
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%0 Journal Article
%A Angulo Pava,  Jaime
%T Stability of solitary wave solutions for equations of short and long dispersive waves
%J Electronic journal of differential equations
%D 2006
%V 2006
%U http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a111/
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%F EJDE_2006__2006__a111
Angulo Pava,  Jaime. Stability of solitary wave solutions for equations of short and long dispersive waves. Electronic journal of differential equations, Tome 2006 (2006). http://geodesic.mathdoc.fr/item/EJDE_2006__2006__a111/