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Quasi‐Periodic Solutions of Nonlinear Evolution Equations Associated with a 3 × 3 Matrix Spectral Problem
Author(s) -
Geng Xianguo,
Wu Lihua,
He Guoliang
Publication year - 2011
Publication title -
studies in applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.164
H-Index - 46
eISSN - 1467-9590
pISSN - 0022-2526
DOI - 10.1111/j.1467-9590.2010.00513.x
Subject(s) - meromorphic function , mathematics , algebraic curve , theta function , nonlinear system , hierarchy , matrix (chemical analysis) , polynomial , algebraic number , function (biology) , pure mathematics , algebraic function , mathematical analysis , algebra over a field , physics , materials science , quantum mechanics , evolutionary biology , economics , market economy , composite material , biology
A hierarchy of new nonlinear evolution equations associated with a 3 × 3 matrix spectral problem with three potentials is proposed. With the aid of the characteristic polynomial of Lax matrix for the hierarchy, we introduce an algebraic curve of arithmetic genus m − 1 , and discuss in detail the properties of the associated Baker–Akhiezer function and meromorphic function. On the basis of the theory of algebraic curves, we obtain the explicit theta function representations of the Baker–Akhiezer function, the meromorphic function, and, in particular, that of solutions for the entire hierarchy of nonlinear evolution equations.