GBDT version of the Darboux transformation for the matrix coupled dispersionless equations (local and non-local cases) | Zendy

Roman O. Popovych | Zendy; Alexander Sakhnovich | Zendy

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GBDT version of the Darboux transformation for the matrix coupled dispersionless equations (local and non-local cases)

Author(s) -

Roman O. Popovych,

Alexander Sakhnovich

Publication year - 2020

Publication title -

journal of integrable systems

Language(s) - English

Resource type - Journals

ISSN - 2058-5985

DOI - 10.1093/integr/xyaa004

Subject(s) - darboux integral , multipole expansion , mathematics , scalar (mathematics) , transformation (genetics) , matrix (chemical analysis) , mathematical physics , algebra over a field , pure mathematics , mathematical analysis , physics , quantum mechanics , geometry , biochemistry , chemistry , materials science , curvature , composite material , gene

We introduce matrix coupled (local and non-local) dispersionless equations, construct GBDT (generalized Bäcklund-Darboux transformation) for these equations, derive wide classes of explicit multipole solutions, give explicit expressions for the corresponding Darboux and wave matrix valued functions and study their asymptotics in some interesting cases. We consider the scalar cases of coupled, complex coupled and non-local dispersionless equations as well.

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