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Complex analysis and mathematical physics
April 20, 2021 16:00, Moscow, online
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On solutions of the matrix nonlinear Schrödinger equation
A. V. Domrin Lomonosov Moscow State University, Faculty of Mechanics and Mathematics
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This page: | 291 |
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Abstract:
Let MnkMnk be the set of all complex n×kn×k-matrices. Consider the
equation iut=uxx+uAu∗Buiut=uxx+uAu∗Bu for an unknown MnkMnk-valued function
u(x,t)u(x,t) of two real variables x,tx,t, where A∈MkkA∈Mkk and B∈MnnB∈Mnn
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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