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Hamiltonian Methods in the Theory of Solitons [electronic resource] / by Ludwig D. Faddeev, Leon A. Takhtajan.

By: Faddeev, Ludwig D [author.].
Contributor(s): Takhtajan, Leon A [author.] | SpringerLink (Online service).
Material type: TextTextSeries: Classics in Mathematics: Publisher: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2007Description: IX, 594 p. 8 illus. online resource.Content type: text Media type: computer Carrier type: online resourceISBN: 9783540699699.Subject(s): Differential equations, partial | Integral equations | Global analysis | Theoretical, Mathematical and Computational Physics | Partial Differential Equations | Integral Equations | Global Analysis and Analysis on ManifoldsAdditional physical formats: Printed edition:: No title; Printed edition:: No title; Printed edition:: No titleDDC classification: 530.1 Online resources: Click here to access online
Contents:
The Nonlinear Schrödinger Equation (NS Model) -- Zero Curvature Representation -- The Riemann Problem -- The Hamiltonian Formulation -- General Theory of Integrable Evolution Equations -- Basic Examples and Their General Properties -- Fundamental Continuous Models -- Fundamental Models on the Lattice -- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models -- Conclusion -- Conclusion.
In: Springer eBooksSummary: The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.
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The Nonlinear Schrödinger Equation (NS Model) -- Zero Curvature Representation -- The Riemann Problem -- The Hamiltonian Formulation -- General Theory of Integrable Evolution Equations -- Basic Examples and Their General Properties -- Fundamental Continuous Models -- Fundamental Models on the Lattice -- Lie-Algebraic Approach to the Classification and Analysis of Integrable Models -- Conclusion -- Conclusion.

The main characteristic of this now classic exposition of the inverse scattering method and its applications to soliton theory is its consistent Hamiltonian approach to the theory. The nonlinear Schrödinger equation, rather than the (more usual) KdV equation, is considered as a main example. The investigation of this equation forms the first part of the book. The second part is devoted to such fundamental models as the sine-Gordon equation, Heisenberg equation, Toda lattice, etc, the classification of integrable models and the methods for constructing their solutions.

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