On the decoupling problem of general quasilinear first order systems in two independent variables

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• 作者：M. Gorgone ^{mgorgone@unime.it" class="auth_mail" title="E-mail the corresponding author} ; F. Oliveri ; ^{foliveri@unime.it" class="auth_mail" title="E-mail the corresponding author} ; M.P. Speciale ^{mpspeciale@unime.it" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Quasilinear first order systems ; Block triangular systems ; Partially decoupled systems ; Block diagonal systems ; Fully decoupled systems
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：446
• 期：1
• 页码：276-298
• 全文大小：446 K

文摘

The paper deals with the decoupling problem of general quasilinear first order systems in two independent variables. We consider either the case of homogeneous and autonomous systems or the one of nonhomogeneous and/or nonautonomous systems. Necessary and sufficient conditions for the partial or full decoupling of the systems at hand are provided. The conditions involve the properties of eigenvalues and eigenvectors of the coefficient matrix, and provide the differential constraints whose integration leads to the decoupling transformation. Some applications of physical interest are also given.