Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-06-20
Nonlinear Sciences
Exactly Solvable and Integrable Systems
19 pages
Scientific paper
10.1016/S0375-9601(01)00366-8
Inverse scattering transform method of the heat equation is developed for a special subclass of potentials nondecaying at space infinity---perturbations of the one-soliton potential by means of decaying two-dimensional functions. Extended resolvent, Green's functions, and Jost solutions are introduced and their properties are investigated in detail. The singularity structure of the spectral data is given and then the Inverse problem is formulated in an exact distributional sense.
Boiti Marco
Pempinelli Flora
Pogrebkov Andrei K.
Prinari Barbara
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