# Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schroedinger systems

## Abstract

Recently, Skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schroedinger equations (NLSEs) describing a binary mixture of Bose-Einstein condensates [see Battye et al., Phys. Rev. Lett. 88, 080401 (2002) and Savage and Ruostekoski, Phys. Rev. Lett. 91, 010403 (2003)] Besides, half-Skyrmions characterized by half-integer topological charges can also be found in the nonlinear {sigma} model which is a model of the Bose-Einstein condensate of the Schwinger bosons [see Morinari, Phys. Rev. B 72, 104502 (2005)]. Here we prove rigorously the existence of half-Skyrmions which may come from a new type of soliton solutions called spike-vortex solutions of two-component systems of NLSE on the entire plane R{sup 2}. These spike-vortex solutions having spikes in one component and a vortex in the other component may form half-Skyrmions. By Liapunov-Schmidt reduction process, we may find spike-vortex solutions of two-component systems of NLSE.

- Authors:

- Department of Mathematics, National Taiwan University, Taipei 106, Taiwan (China) and National Center of Theoretical Sciences, National Tsing Hua University, Hsinchu, Taiwan 30043 (China)
- (China)

- Publication Date:

- OSTI Identifier:
- 20929726

- Resource Type:
- Journal Article

- Resource Relation:
- Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2722559; (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; AXIOMATIC FIELD THEORY; BINARY MIXTURES; BOSE-EINSTEIN CONDENSATION; BOSONS; MATHEMATICAL SOLUTIONS; NONLINEAR PROBLEMS; SCHROEDINGER EQUATION; SCHWINGER SOURCE THEORY; SIGMA MODEL; SKYRME POTENTIAL; SOLITONS; TOPOLOGY

### Citation Formats

```
Lin, T.-C., Wei Juncheng, and Department of Mathematics, hinese University of Hong Kong, Shatin, Hong Kong.
```*Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schroedinger systems*. United States: N. p., 2007.
Web. doi:10.1063/1.2722559.

```
Lin, T.-C., Wei Juncheng, & Department of Mathematics, hinese University of Hong Kong, Shatin, Hong Kong.
```*Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schroedinger systems*. United States. doi:10.1063/1.2722559.

```
Lin, T.-C., Wei Juncheng, and Department of Mathematics, hinese University of Hong Kong, Shatin, Hong Kong. Tue .
"Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schroedinger systems". United States.
doi:10.1063/1.2722559.
```

```
@article{osti_20929726,
```

title = {Half-Skyrmions and spike-vortex solutions of two-component nonlinear Schroedinger systems},

author = {Lin, T.-C. and Wei Juncheng and Department of Mathematics, hinese University of Hong Kong, Shatin, Hong Kong},

abstractNote = {Recently, Skyrmions with integer topological charges have been observed numerically but have not yet been shown rigorously on two-component systems of nonlinear Schroedinger equations (NLSEs) describing a binary mixture of Bose-Einstein condensates [see Battye et al., Phys. Rev. Lett. 88, 080401 (2002) and Savage and Ruostekoski, Phys. Rev. Lett. 91, 010403 (2003)] Besides, half-Skyrmions characterized by half-integer topological charges can also be found in the nonlinear {sigma} model which is a model of the Bose-Einstein condensate of the Schwinger bosons [see Morinari, Phys. Rev. B 72, 104502 (2005)]. Here we prove rigorously the existence of half-Skyrmions which may come from a new type of soliton solutions called spike-vortex solutions of two-component systems of NLSE on the entire plane R{sup 2}. These spike-vortex solutions having spikes in one component and a vortex in the other component may form half-Skyrmions. By Liapunov-Schmidt reduction process, we may find spike-vortex solutions of two-component systems of NLSE.},

doi = {10.1063/1.2722559},

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}

}