We consider the existence and stability of traveling waves of a generalized Ostrovsky equation ${(u_t-\beta u_{xxx}-f{\left(u\right)}_x)}_x=\gamma u$, where the nonlinearity $f\left(u\right)$ 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.

中文翻译：

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广义 Ostrovsky 方程的孤立波

我们考虑广义 Ostrovsky 方程行波的存在性和稳定性 ${({你}_{吨}-\beta {你}_{XXX}-F{\left(你\right)}_X)}_X=\gamma 你$，其中非线性 $F\left(你\right)$满足类似幂的缩放条件。我们证明存在最小化所有非平凡解之间作用的基态解，并使用这种变分表征来研究它们的稳定性。我们还介绍了一种基于变分特性计算基态的数值方法。所考虑的非线性类别包括不同幂的和和差。