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Bibliographic Details
Main Authors: Smirnov, Aleksandr O., Caplieva, Aleksandra A.
Format: Preprint
Published: 2022
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Online Access:https://arxiv.org/abs/2211.12895
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author Smirnov, Aleksandr O.
Caplieva, Aleksandra A.
author_facet Smirnov, Aleksandr O.
Caplieva, Aleksandra A.
contents In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations.
format Preprint
id arxiv_https___arxiv_org_abs_2211_12895
institution arXiv
publishDate 2022
record_format arxiv
spellingShingle The vector form of Kundu-Eckhaus equation and its simplest solutions
Smirnov, Aleksandr O.
Caplieva, Aleksandra A.
Exactly Solvable and Integrable Systems
Mathematical Physics
In our work a hierarchy of integrable vector nonlinear differential equations depending on the functional parameter $r$ is constructed using a monodromy matrix. The first equation of this hierarchy for $r=α(\mathbf{p}^t\mathbf{q})$ is vector analogue of the Kundu-Eckhaus equation. When $α=0$, the equations of this hierarchy turn into equations of the Manakov system hierarchy. New elliptic solutions to vector analogue of the Kundu-Eckhaus and Manakov system are presented. In conclusion, it is shown that there exist linear transformations of solutions to vector integrable nonlinear equations into other solutions to the same equations.
title The vector form of Kundu-Eckhaus equation and its simplest solutions
topic Exactly Solvable and Integrable Systems
Mathematical Physics
url https://arxiv.org/abs/2211.12895