The Kawahara–Korteweg–de Vries-type equation occurs in the modelization of magneto-acoustic waves in plasmas and propagation of nonlinear water waves in the long-wavelength region as in the case of Korteweg–de Vries equation. In this paper, we prove the well-posedness of the classical solutions for the Cauchy problem associated with this equation.

中文翻译：

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Kawahara–Korteweg–de Vries型方程经典解的适定性

Kawahara–Korteweg–de Vries型方程式发生在等离子体中的磁声波建模以及非线性水波在长波长区域中的传播，就像Korteweg–de Vries方程式一样。在本文中，我们证明了与此方程有关的柯西问题的经典解的适定性。