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On effective solution for some class of vector boundary Riemann problem and corresponding algebraic equations
Author(s) -
Dmitriyeva I.
Publication year - 1998
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19980781521
Subject(s) - mathematics , riemann problem , pure mathematics , algebraic solution , mathematical analysis , boundary (topology) , class (philosophy) , constructive , matrix (chemical analysis) , boundary value problem , algebraic number , riemann sphere , riemann surface , riemann hypothesis , algebra over a field , differential equation , differential algebraic equation , ordinary differential equation , materials science , process (computing) , artificial intelligence , computer science , composite material , operating system
The special class of homogeneous vector boundary Riemann problem on the finite sequence of compact Riemann surfaces is investigated completely. Its coefficients are noncommutative permutation matrices of the arbitrary but not prime order, and boundary conditions are given on the system of open contours. The constructive algorithm and definite structure of the canonical solution matrix are obtained explicitly and present the considerable generalization of paper [1]. Simultaneously the corresponding class of algebraic equations for the appropriate covering surfaces is formed in obvious way too. The suggested applications concern mostly the solitary waves' theory and inverse scattering problem in particular (e. g. see [2]).