We consider the existence and stability of traveling waves of the Fifth-Order KdV equation for a general class of nonlinearities that satisfy power-like scaling relations. This class of nonlinearities includes sums and differences of powers. For such nonlinearities we use variational methods to show that there exist ground state traveling wave solutions and use the variational properties of the ground states to analyze their stability.

中文翻译：

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五阶KdV方程行波的存在性和稳定性

对于满足幂次标度关系的一般非线性，我们考虑了五阶KdV方程行波的存在性和稳定性。这类非线性包括幂的和与差。对于这种非线性，我们使用变分方法来证明存在基态行波解，并使用基态的变分性质来分析其稳定性。