dorsal/arxiv
View SchemaA Potential of Interaction between Two- and Three-Dimensional Solitons
| Authors | Boris A. Malomed |
|---|---|
| Categories | |
| ArXiv ID | patt-sol/9809009 |
| URL | https://arxiv.org/abs/patt-sol/9809009 |
| DOI | 10.1103/PhysRevE.58.7928 |
Abstract
A general method to find an effective potential of interaction between far separated 2D and 3D solitons is elaborated, including the case of 2D vortex solitons. The method is based on explicit calculation of the overlapping term in the full Hamiltonian of the system (_without_ assuming that the ``tail'' of each soliton is not affected by its interaction with the other soliton, and, in fact,_without_ knowing the exact form of the solution for an isolated soliton - the latter problem is circumvented by reducing a bulk integral to a surface one). The result is obtained in an explicit form that does not contain an artificially introduced radius of the overlapping region. The potential applies to spatial and spatiotemporal solitons in nonlinear optics, where it may help to solve various dynamical problems: collisions, formation of bound states (BS's), etc. In particular, an orbiting BS of two solitons is always unstable. In the presence of weak dissipation and gain, the effective potential can also be derived, giving rise to bound states similar to those recently studied in 1D models.
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"abstract": "A general method to find an effective potential of interaction between far\nseparated 2D and 3D solitons is elaborated, including the case of 2D vortex\nsolitons. The method is based on explicit calculation of the overlapping term\nin the full Hamiltonian of the system (_without_ assuming that the ``tail\u0027\u0027 of\neach soliton is not affected by its interaction with the other soliton, and, in\nfact,_without_ knowing the exact form of the solution for an isolated soliton -\nthe latter problem is circumvented by reducing a bulk integral to a surface\none). The result is obtained in an explicit form that does not contain an\nartificially introduced radius of the overlapping region. The potential applies\nto spatial and spatiotemporal solitons in nonlinear optics, where it may help\nto solve various dynamical problems: collisions, formation of bound states\n(BS\u0027s), etc. In particular, an orbiting BS of two solitons is always unstable.\nIn the presence of weak dissipation and gain, the effective potential can also\nbe derived, giving rise to bound states similar to those recently studied in 1D\nmodels.",
"arxiv_id": "patt-sol/9809009",
"authors": [
"Boris A. Malomed"
],
"categories": [
"patt-sol",
"nlin.PS"
],
"doi": "10.1103/PhysRevE.58.7928",
"title": "A Potential of Interaction between Two- and Three-Dimensional Solitons",
"url": "https://arxiv.org/abs/patt-sol/9809009"
},
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