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 Schrรถdinger 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
CONTENT
The Nonlinear Schrรถdinger 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
Physics
Global analysis (Mathematics)
Manifolds (Mathematics)
Integral equations
Partial differential equations
Physics
Theoretical Mathematical and Computational Physics
