# Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schroedinger equations

## Abstract

In this paper we consider generalized nonlinear Schroedinger equations with external potentials. We find the expressions for the fourth and the sixth order Fermi golden rules (FGRs), conjectured in Gang and Sigal [Rev. Math. Phys. 17, 1143-1207 (2005); Geom. Funct. Anal. 16, No. 7, 1377-1390 (2006)]. The FGR is a key condition in a study of the asymptotic dynamics of trapped solitons.

- Authors:

- Department of Mathematics, University of Toronto, Toronto, Ontario M5S 2E4 (Canada)

- Publication Date:

- OSTI Identifier:
- 20929720

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2716971; (c) 2007 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; NONLINEAR PROBLEMS; PERTURBATION THEORY; POTENTIALS; SCHROEDINGER EQUATION; SOLITONS

### Citation Formats

```
Zhou Gang.
```*Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schroedinger equations*. United States: N. p., 2007.
Web. doi:10.1063/1.2716971.

```
Zhou Gang.
```*Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schroedinger equations*. United States. doi:10.1063/1.2716971.

```
Zhou Gang. Tue .
"Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schroedinger equations". United States.
doi:10.1063/1.2716971.
```

```
@article{osti_20929720,
```

title = {Perturbation expansion and Nth order Fermi golden rule of the nonlinear Schroedinger equations},

author = {Zhou Gang},

abstractNote = {In this paper we consider generalized nonlinear Schroedinger equations with external potentials. We find the expressions for the fourth and the sixth order Fermi golden rules (FGRs), conjectured in Gang and Sigal [Rev. Math. Phys. 17, 1143-1207 (2005); Geom. Funct. Anal. 16, No. 7, 1377-1390 (2006)]. The FGR is a key condition in a study of the asymptotic dynamics of trapped solitons.},

doi = {10.1063/1.2716971},

journal = {Journal of Mathematical Physics},

number = 5,

volume = 48,

place = {United States},

year = {Tue May 15 00:00:00 EDT 2007},

month = {Tue May 15 00:00:00 EDT 2007}

}

DOI: 10.1063/1.2716971

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