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Analytic-Bilinear Approach to Integrable Hierarchies (Hardcover, 1999 ed.)
Loot Price: R1,630
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Analytic-Bilinear Approach to Integrable Hierarchies (Hardcover, 1999 ed.)
Series: Mathematics and Its Applications, 493
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Total price: R1,650
Discovery Miles: 16 500
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The subject of this book is the hierarchies of integrable equations
connected with the one-component and multi component loop groups.
There are many publications on this subject, and it is rather well
defined. Thus, the author would like t.o explain why he has taken
the risk of revisiting the subject. The Sato Grassmannian approach,
and other approaches standard in this context, reveal deep
mathematical structures in the base of the integrable hi erarchies.
These approaches concentrate mostly on the algebraic picture, and
they use a language suitable for applications to quantum field
theory. Another well-known approach, the a-dressing method,
developed by S. V. Manakov and V.E. Zakharov, is oriented mostly to
particular systems and ex act classes of their solutions. There is
more emphasis on analytic properties, and the technique is
connected with standard complex analysis. The language of the
a-dressing method is suitable for applications to integrable
nonlinear PDEs, integrable nonlinear discrete equations, and, as
recently discovered, for t.he applications of integrable systems to
continuous and discret.e geometry. The primary motivation of the
author was to formalize the approach to int.e grable hierarchies
that was developed in the context of the a-dressing method,
preserving the analytic struetures characteristic for this method,
but omitting the peculiarit.ies of the construetive scheme. And it
was desirable to find a start."
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