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Complex analysis and mathematical physics
April 20, 2021 16:00, Moscow, online
 


On solutions of the matrix nonlinear Schrödinger equation

A. V. Domrin

Lomonosov Moscow State University, Faculty of Mechanics and Mathematics

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Abstract: Let MnkMnk be the set of all complex n×kn×k-matrices. Consider the equation iut=uxx+uAuBuiut=uxx+uAuBu for an unknown MnkMnk-valued function u(x,t)u(x,t) of two real variables x,tx,t, where AMkkAMkk and BMnnBMnn are non-degenerate Hermitian matrices and the star stands for Hermitian conjugation. We prove that every real analytic solution is a globally meromorphic function of xx for every fixed tt. When all the eigenvalues of both matrices A,BA,B are of the same sign, every local real analytic solution extends to a real analytic function in a strip (depending on the solution) parallel to the xx-axis (possibly a half-plane or the whole plane), and every such strip carries a solution inextensible beyond it.

Website: https://mi-ras-ru.zoom.us/j/6119310351?pwd=anpleGlnYVFXNEJnemRYZk5kMWNiQT09

* ID: 611 931 0351. Password: 5MAVBP.
 
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