### Abstract

We obtain analytical expressions for an effective potential of interaction between two-and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by cross-phase modulation. The derivation is based on calculation of the interaction term in the full Hamiltonian of the system. An essential peculiarity is that, in the 3D case, as well as in the case of 2D solitons with unequal masses, the main contribution to the interaction potential originates from a vicinity of one or both solitons, similarly to what was recently found in the 2D and 3D single-mode systems, while in the case of identical 2D solitons, the dominating area covers all the space between the solitons. Unlike the single-mode systems, stable bound states of mutually orbiting solitons are possible in the bimodal system.

Original language | English |
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Pages (from-to) | 179-184 |

Number of pages | 6 |

Journal | Physics Letters, Section A: General, Atomic and Solid State Physics |

Volume | 254 |

Issue number | 3-4 |

Publication status | Published - Apr 12 1999 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)

### Cite this

*Physics Letters, Section A: General, Atomic and Solid State Physics*,

*254*(3-4), 179-184.

**A potential of incoherent attraction between multidimensional solitons.** / Maimistov, Andrey; Malomed, Boris; Desyatnikov, Anton.

Research output: Contribution to journal › Article

*Physics Letters, Section A: General, Atomic and Solid State Physics*, vol. 254, no. 3-4, pp. 179-184.

}

TY - JOUR

T1 - A potential of incoherent attraction between multidimensional solitons

AU - Maimistov, Andrey

AU - Malomed, Boris

AU - Desyatnikov, Anton

PY - 1999/4/12

Y1 - 1999/4/12

N2 - We obtain analytical expressions for an effective potential of interaction between two-and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by cross-phase modulation. The derivation is based on calculation of the interaction term in the full Hamiltonian of the system. An essential peculiarity is that, in the 3D case, as well as in the case of 2D solitons with unequal masses, the main contribution to the interaction potential originates from a vicinity of one or both solitons, similarly to what was recently found in the 2D and 3D single-mode systems, while in the case of identical 2D solitons, the dominating area covers all the space between the solitons. Unlike the single-mode systems, stable bound states of mutually orbiting solitons are possible in the bimodal system.

AB - We obtain analytical expressions for an effective potential of interaction between two-and three-dimensional (2D and 3D) solitons (including the case of 2D vortex solitons) belonging to two different modes which are incoherently coupled by cross-phase modulation. The derivation is based on calculation of the interaction term in the full Hamiltonian of the system. An essential peculiarity is that, in the 3D case, as well as in the case of 2D solitons with unequal masses, the main contribution to the interaction potential originates from a vicinity of one or both solitons, similarly to what was recently found in the 2D and 3D single-mode systems, while in the case of identical 2D solitons, the dominating area covers all the space between the solitons. Unlike the single-mode systems, stable bound states of mutually orbiting solitons are possible in the bimodal system.

UR - http://www.scopus.com/inward/record.url?scp=0042781044&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0042781044&partnerID=8YFLogxK

M3 - Article

VL - 254

SP - 179

EP - 184

JO - Physics Letters, Section A: General, Atomic and Solid State Physics

JF - Physics Letters, Section A: General, Atomic and Solid State Physics

SN - 0375-9601

IS - 3-4

ER -