具有空间记忆的Ostrovsky-Whitham型弛豫介质动力系统的解析性质及其可积正则化
Analytical Properties of an Ostrovsky-Whitham Type Dynamical System for a Relaxing Medium with Spatial Memory and its Integrable Regularization
摘要：
弛豫介质中的短波扰动，由奥斯特洛夫斯基演化方程的特殊简化决定，后来由Whitham导出，利用梯度-完整可积算法研究了两个动力系统的双Hamilton性和完全可积性，得到了两个和四个相互交换的色散型守恒律的无限族，并讨论了它们的双Hamilton性和完全可积性。详细研究了维数不变约简。构造了模型的正则化，讨论了正则化的Lax型可积性.
英文摘要：
Short-wave perturbations in a relaxing medium, governed by a special reduction of the Ostrovsky evolution equation, and later derived by Whitham, are studied using the gradient-holonomic integrability algorithm.The bi-Hamiltonicity and complete integrability of the corresponding dynamical system is stated and an infinite hierarchy of commuting to each other conservation laws of dispersive type are found. The two- and four-dimensional invariant reductions are studied in detail. The well defined regularization of the model is constructed and its Lax type integrability is discussed.
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