Abstract
We obtain conditions for the nonlinear stability (Theorem 5.1) of solitary waves fro two classes of nonlinear dispersive equations which arise in the mathematical description of long wave propagation:(u is in general complex-valued), where the linear operator L, typically nonlocal, and the nonlinearity, are of some general class.For the case of homogeneous nonlinearities, A(u), a new variational characterization of solitary waves for I and II is presented (Theorem 3.1) and is exploited in the dynamic stability analysis. The existence of solitary waves in higher dimensions is also considered (Theorem 7.1).
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