Stability of solitary wave solutions for equations of short and long dispersive waves
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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.