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Many physical phenomena are described by nonlinear evolution
equation. Those that are integrable provide various mathematical
methods, presented by experts in this tutorial book, to find
special analytic solutions to both integrable and partially
integrable equations. The direct method to build solutions includes
the analysis of singularities a la Painleve, Lie symmetries leaving
the equation invariant, extension of the Hirota method,
construction of the nonlinear superposition formula. The main
inverse method described here relies on the bi-hamiltonian
structure of integrable equations. The book also presents some
extension to equations with discrete independent and dependent
variables.
The different chapters face from different points of view the
theory of exact solutions and of the complete integrability of
nonlinear evolution equations. Several examples and applications to
concrete problems allow the reader to experience directly the power
of the different machineries involved."
Many physical phenomena are described by nonlinear evolution
equation. Those that are integrable provide various mathematical
methods, presented by experts in this tutorial book, to find
special analytic solutions to both integrable and partially
integrable equations. The direct method to build solutions includes
the analysis of singularities a la Painleve, Lie symmetries leaving
the equation invariant, extension of the Hirota method,
construction of the nonlinear superposition formula. The main
inverse method described here relies on the bi-hamiltonian
structure of integrable equations. The book also presents some
extension to equations with discrete independent and dependent
variables.
The different chapters face from different points of view the
theory of exact solutions and of the complete integrability of
nonlinear evolution equations. Several examples and applications to
concrete problems allow the reader to experience directly the power
of the different machineries involved."
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