### Abstract

We demonstrate analytically that the effective potential of interaction between widely separated solitons in a damped, ac-driven nonlinear Schrödinger equation is oscillatory at large distances. We show numerically that two solitons in the system attract each other if the initial distance between them is smaller than a certain critical value; consequently, they will either form an oscillatory bound state with a finite lifetime, collapse to a stable single soliton state, or decay to the rotating background. If the initial separation is greater than the critical value, they separate to form a stable bound state at a second critical distance. The critical distances are in good agreement with the analytical prediction.

Original language | English (US) |
---|---|

Pages (from-to) | 1677-1679 |

Number of pages | 3 |

Journal | Physical Review E |

Volume | 49 |

Issue number | 2 |

DOIs | |

State | Published - 1994 |

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### ASJC Scopus subject areas

- Mathematical Physics
- Physics and Astronomy(all)
- Condensed Matter Physics
- Statistical and Nonlinear Physics

### Cite this

*Physical Review E*,

*49*(2), 1677-1679. https://doi.org/10.1103/PhysRevE.49.1677

**Bound solitons in the ac-driven, damped nonlinear Schrödinger equation.** / Cai, David; Bishop, A. R.; Grønbech-Jensen, Niels; Malomed, Boris A.

Research output: Contribution to journal › Article

*Physical Review E*, vol. 49, no. 2, pp. 1677-1679. https://doi.org/10.1103/PhysRevE.49.1677

}

TY - JOUR

T1 - Bound solitons in the ac-driven, damped nonlinear Schrödinger equation

AU - Cai, David

AU - Bishop, A. R.

AU - Grønbech-Jensen, Niels

AU - Malomed, Boris A.

PY - 1994

Y1 - 1994

N2 - We demonstrate analytically that the effective potential of interaction between widely separated solitons in a damped, ac-driven nonlinear Schrödinger equation is oscillatory at large distances. We show numerically that two solitons in the system attract each other if the initial distance between them is smaller than a certain critical value; consequently, they will either form an oscillatory bound state with a finite lifetime, collapse to a stable single soliton state, or decay to the rotating background. If the initial separation is greater than the critical value, they separate to form a stable bound state at a second critical distance. The critical distances are in good agreement with the analytical prediction.

AB - We demonstrate analytically that the effective potential of interaction between widely separated solitons in a damped, ac-driven nonlinear Schrödinger equation is oscillatory at large distances. We show numerically that two solitons in the system attract each other if the initial distance between them is smaller than a certain critical value; consequently, they will either form an oscillatory bound state with a finite lifetime, collapse to a stable single soliton state, or decay to the rotating background. If the initial separation is greater than the critical value, they separate to form a stable bound state at a second critical distance. The critical distances are in good agreement with the analytical prediction.

UR - http://www.scopus.com/inward/record.url?scp=0000954795&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0000954795&partnerID=8YFLogxK

U2 - 10.1103/PhysRevE.49.1677

DO - 10.1103/PhysRevE.49.1677

M3 - Article

VL - 49

SP - 1677

EP - 1679

JO - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

JF - Physical Review E - Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics

SN - 1063-651X

IS - 2

ER -