# Stabilization of high-order solutions of the cubic nonlinear Schroedinger equation

## Abstract

In this paper we consider the stabilization of nonfundamental unstable stationary solutions of the cubic nonlinear Schroedinger equation. Specifically, we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones, we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible.

- Authors:

- Departamento de Matematicas, E. T. S. Ingenieros Industriales and Instituto de Matematica Aplicada a la Ciencia y la Ingenieria (IMACI), Avda. Camilo Jose Cela, 3, Universidad de Castilla-La Mancha, 13071 Ciudad Real (Spain)

- Publication Date:

- OSTI Identifier:
- 21072426

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics; Journal Volume: 75; Journal Issue: 4; Other Information: DOI: 10.1103/PhysRevE.75.046609; (c) 2007 The American Physical Society; Country of input: International Atomic Energy Agency (IAEA)

- Country of Publication:
- United States

- Language:
- English

- Subject:
- 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMMETRY; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; QUANTUM MECHANICS; SCHROEDINGER EQUATION; STABILIZATION; VORTICES

### Citation Formats

```
Alexandrescu, Adrian, Montesinos, Gaspar D., and Perez-Garcia, Victor M..
```*Stabilization of high-order solutions of the cubic nonlinear Schroedinger equation*. United States: N. p., 2007.
Web. doi:10.1103/PHYSREVE.75.046609.

```
Alexandrescu, Adrian, Montesinos, Gaspar D., & Perez-Garcia, Victor M..
```*Stabilization of high-order solutions of the cubic nonlinear Schroedinger equation*. United States. doi:10.1103/PHYSREVE.75.046609.

```
Alexandrescu, Adrian, Montesinos, Gaspar D., and Perez-Garcia, Victor M.. Sun .
"Stabilization of high-order solutions of the cubic nonlinear Schroedinger equation". United States.
doi:10.1103/PHYSREVE.75.046609.
```

```
@article{osti_21072426,
```

title = {Stabilization of high-order solutions of the cubic nonlinear Schroedinger equation},

author = {Alexandrescu, Adrian and Montesinos, Gaspar D. and Perez-Garcia, Victor M.},

abstractNote = {In this paper we consider the stabilization of nonfundamental unstable stationary solutions of the cubic nonlinear Schroedinger equation. Specifically, we study the stabilization of radially symmetric solutions with nodes and asymmetric complex stationary solutions. For the first ones, we find partial stabilization similar to that recently found for vortex solutions while for the later ones stabilization does not seem possible.},

doi = {10.1103/PHYSREVE.75.046609},

journal = {Physical Review. E, Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics},

number = 4,

volume = 75,

place = {United States},

year = {Sun Apr 15 00:00:00 EDT 2007},

month = {Sun Apr 15 00:00:00 EDT 2007}

}

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