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|Type:||Artigo de periódico|
|Title:||Existence and stability of periodic travelling-wave solutions of the Benjamin equation|
|Abstract:||A family of steady periodic water waves in very deep fluids when the surface tension is present and satisfying the following nonlinear pseudo-differential equation u(t) + uu(x) + u(xxx) + lHu(xx) = 0, known as the Benjamin equation, is shown to exist. Here H denotes the periodic Hilbert transform and l is an element of R. By fixing a minimal period we obtain, via the implicit function theorem, an analytic curve of periodic travelling-wave solutions depending on the parameter l. Moreover, by making some changes in the abstract stability theory developed by Grillakis, Shatah, and Strauss, we prove that these travelling waves are nonlinearly stable to perturbations with the same wavelength.|
|Editor:||Amer Inst Mathematical Sciences|
|Appears in Collections:||Unicamp - Artigos e Outros Documentos|
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