Nonlinear coupled wave propagation in a n-dimensional layer

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• 作者：Yury G. Smirnov ^{smirnovyug@mail.ru" class="auth_mail" title="E-mail the corresponding author} ; Dmitry V. Valovik ; ^{dvalovik@mail.ru" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Nonlinear multi-parameter eigenvalue problem ; Linear multi-parameter eigenvalue problem ; Eigentuples ; Maxwell&rsquo ; s equations ; Nonlinear guided wave ; Dispersion equation
• 刊名：Applied Mathematics and Computation
• 出版年：2017
• 出版时间：1 February 2017
• 年：2017
• 卷：294
• 期：Complete
• 页码：146-156
• 全文大小：427 K

文摘

The paper focuses on the generalization of a nonlinear multi-parameter eigenvalue problem for a system of nonlinear differential equations. The problem is reduced to a system of nonlinear integral equations on a segment. The notion of eigentuple is introduced, the existence of a finite number of isolated eigentuples is proved, and their distribution is described. The corresponding linear multi-parameter eigenvalue problem is studied as well; it is proved that the linear problem has an infinite number of isolated eigentuples. Applications to nonlinear electromagnetic wave propagation theory are demonstrated.