利用复李对称对微分方程组进行线性化——II：偏微分方程
经典分析与常微分方程
2011-07-25 v2
摘要
通过将李线性化判据推广到复变量的复函数，研究了复常微分方程的线性化。证明了复常微分方程的线性化意味着与这些复常微分方程相对应的偏微分方程组的可线性化性。可逆的复变换可用于获得可逆的实变换，将非线性偏微分方程组映射为线性偏微分方程组。给出了明确的不变准则，为写出线性化方程的解提供了方法。提及了一些非平凡的例子。
引用
@article{arxiv.0711.4921,
title = {Use of Complex Lie Symmetries for Linearization of Systems of Differential Equations - II: Partial Differential Equations},
author = {S. Ali and F. M. Mahomed and Asghar Qadir},
journal= {arXiv preprint arXiv:0711.4921},
year = {2011}
}
备注
This paper along with its first part ODE-I were combined in a single research paper "Linearizability criteria for systems of two second-order differential equations by complex methods" which has been published in Nonlinear Dynamics. Due to citations of both parts I and II these are not replaced with the above published article