Solitary waves of a generalized Ostrovsky equation

Abstract

We consider the existence and stability of traveling waves of a generalized Ostrovsky equation (ut−βuxxx−f(u)x)x=γu, where the nonlinearity f(u) satisfies a power-like scaling condition. We prove that there exist ground state solutions which minimize the action among all nontrivial solutions and use this variational characterization to study their stability. We also introduce a numerical method for computing ground states based on their variational properties. The class of nonlinearities considered includes sums and differences of distinct powers.