# Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential

## Abstract

In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.

- Authors:

- Dipartimento di Fisica, Universita di Lecce, Sezione INFN, Lecce I-73100 (Italy)
- (Russian Federation)

- Publication Date:

- OSTI Identifier:
- 20861567

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 47; Journal Issue: 12; Other Information: DOI: 10.1063/1.2393144; (c) 2006 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; EVOLUTION; INVERSE SCATTERING PROBLEM; MATHEMATICAL SOLUTIONS; PERTURBATION THEORY; POTENTIAL SCATTERING; POTENTIALS; SCHROEDINGER EQUATION; SOLITONS

### Citation Formats

```
Boiti, M., Pempinelli, F., Pogrebkov, A. K., and Steklov Mathematical Institute, 119991 Moscow.
```*Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential*. United States: N. p., 2006.
Web. doi:10.1063/1.2393144.

```
Boiti, M., Pempinelli, F., Pogrebkov, A. K., & Steklov Mathematical Institute, 119991 Moscow.
```*Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential*. United States. doi:10.1063/1.2393144.

```
Boiti, M., Pempinelli, F., Pogrebkov, A. K., and Steklov Mathematical Institute, 119991 Moscow. Fri .
"Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential". United States.
doi:10.1063/1.2393144.
```

```
@article{osti_20861567,
```

title = {Scattering transform for nonstationary Schroedinger equation with bidimensionally perturbed N-soliton potential},

author = {Boiti, M. and Pempinelli, F. and Pogrebkov, A. K. and Steklov Mathematical Institute, 119991 Moscow},

abstractNote = {In the framework of the extended resolvent approach the direct and inverse scattering problems for the nonstationary Schroedinger equation with a potential being a perturbation of the N-soliton potential by means of a generic bidimensional smooth function decaying at large spaces are introduced and investigated. The initial value problem of the Kadomtsev-Petviashvili I equation for a solution describing N wave solitons on a generic smooth decaying background is then linearized, giving the time evolution of the spectral data.},

doi = {10.1063/1.2393144},

journal = {Journal of Mathematical Physics},

number = 12,

volume = 47,

place = {United States},

year = {Fri Dec 15 00:00:00 EST 2006},

month = {Fri Dec 15 00:00:00 EST 2006}

}

DOI: 10.1063/1.2393144

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