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Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity
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- Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)
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- Symmetry, Integrability and Geometry: Methods and Applications, 2015, том 11
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Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity
Інший ID:
2010 Mathematics Subject Classification: 34L05; 16S32; 37K10
DOI:10.3842/SIGMA.2015.087
DOI:10.3842/SIGMA.2015.087
Посилання:
Bispectrality of N-Component KP Wave Functions: A Study in Non-Commutativity / A. Kasman // Symmetry, Integrability and Geometry: Methods and Applications. — 2015. — Т. 11. — Бібліогр.: 33 назв. — англ.
Підтримка:
The author thanks the College of Charleston for the sabbatical during which this work was
completed, Maarten Bergvelt and Michael Gekhtman for mathematical assistance as well as
serving as gracious hosts, Chunxia Li for carefully reading and commenting on early drafts, and
the referees for their advices.
Дата:
2015
Переглядів:
534
Завантажень:
247
Анотація:
A wave function of the N-component KP Hierarchy with continuous flows determined by an invertible matrix H is constructed from the choice of an MN-dimensional space of finitely-supported vector distributions. This wave function is shown to be an eigenfunction for a ring of matrix differential operators in x having eigenvalues that are matrix functions of the spectral parameter z. If the space of distributions is invariant under left multiplication by H, then a matrix coefficient differential-translation operator in z is shown to share this eigenfunction and have an eigenvalue that is a matrix function of x. This paper not only generates new examples of bispectral operators, it also explores the consequences of non-commutativity for techniques and objects used in previous investigations.
