Integrability of linear and nonlinear evolution equations and the associated nonlinear Fourier transforms. (English) Zbl 0807.35138

Fokas, A. S.; Gelfand, I. M.

Lett. Math. Phys. 32, No. 3, 189-210 (1994).

Summary: The inverse spectral method is a nonlinear Fourier transform method for solving certain equations. Here, we emphasize that such transforms should be considered in their own right. We also elucidate further the connection between the Fourier transform and inverse spectral methods by establishing that linear equations can also be solved through the inverse spectral method.

MSC:

35Q58	Other completely integrable PDE (MSC2000)
37J35	Completely integrable finite-dimensional Hamiltonian systems, integration methods, integrability tests
37K10	Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.)
58J72	Correspondences and other transformation methods (e.g., Lie-Bäcklund) for PDEs on manifolds

Keywords:

inverse spectral method; nonlinear Fourier transform

References:

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