Classification of a class of systems of cubic ordinary differential equations

In this article, we consider the classification of the systems of two ordinary differential equations with a complex-valued unknown and gauge-invariant cubic nonlinearities of polynomial type. The class of systems of ODEs arises in the study of the large time behavior of a system of cubic nonlinear...

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Bibliographic Details
Published inJournal of Differential Equations Vol. 344; pp. 471 - 508
Main Author Masaki, Satoshi
Format Journal Article
LanguageEnglish
Published Elsevier Inc 25.01.2023
Subjects
Classification of systems of cubic ODEs
Classification of systems of cubic PDEs
Classification of systems of cubic ODEs
34A34
35E20
Classification of systems of cubic PDEs
34C20
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Summary:In this article, we consider the classification of the systems of two ordinary differential equations with a complex-valued unknown and gauge-invariant cubic nonlinearities of polynomial type. The class of systems of ODEs arises in the study of the large time behavior of a system of cubic nonlinear Schrödinger equations or that of cubic nonlinear Klein-Gordon equations. We give the complete classification of the systems which possess a conserved quantity of quadratic type. Our argument is based on the representation of a system in terms of a pair of a matrix and a vector.
ISSN:0022-0396
1090-2732
DOI:10.1016/j.jde.2022.11.001