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We consider the existence and stability of traveling waves of a generalized Ostrovsky equation , where the nonlinearity 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. 相似文献
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We consider a reaction–diffusion–advection equation of the form: for , where is a -periodic function, is a -periodic Fisher–KPP type of nonlinearity with changing sign, is a free boundary satisfying the Stefan condition. We study the long time behavior of solutions and find that there are two critical numbers and with , and , such that a vanishing–spreading dichotomy result holds when ; a vanishing–transition–virtual spreading trichotomy result holds when ; all solutions vanish when or . 相似文献