Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2001-01-17
Nonlinear Sciences
Exactly Solvable and Integrable Systems
22 pages, submitted to Inverse Problems
Scientific paper
10.1088/0266-5611/17/4/324
The resolvent approach is applied to the spectral analysis of the heat equation with non decaying potentials. The special case of potentials with spectral data obtained by a rational similarity transformation of the spectral data of a generic decaying potential is considered. It is shown that these potentials describe $N$ solitons superimposed by Backlund transformations to a generic background. Dressing operators and Jost solutions are constructed by solving a DBAR-problem explicitly in terms of the corresponding objects associated to the original potential. Regularity conditions of the potential in the cases N=1 and N=2 are investigated in details. The singularities of the resolvent for the case N=1 are studied, opening the way to a correct definition of the spectral data for a generically perturbed soliton.
Boiti Marco
Pempinelli Flora
Pogrebkov Andrei K.
Prinari Barbara
No associations
LandOfFree
Towards an Inverse Scattering theory for non decaying potentials of the heat equation does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Towards an Inverse Scattering theory for non decaying potentials of the heat equation, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Towards an Inverse Scattering theory for non decaying potentials of the heat equation will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-296314