Soliton lattices in the Gross–Pitaevskii equation with nonlocal and repulsive coupling

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Abstract

Spatially-periodic patterns are studied in nonlocally coupled Gross–Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole–dipole interaction. Next, we study a model with a finite-range coupling, and show that a repulsively coupled system is closely related with an attractively coupled system and its soliton solution becomes a building block of the spatially-periodic structure. That is, the spatially-periodic structure can be interpreted as a soliton lattice. An approximate form of the soliton is given by a variational method. Furthermore, the effects of the rotating harmonic potential and spin-orbit coupling are numerically studied.

Original languageEnglish
Pages (from-to)1132-1137
Number of pages6
JournalPhysics Letters, Section A: General, Atomic and Solid State Physics
Volume383
Issue number11
DOIs
Publication statusPublished - Mar 25 2019

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solitary waves
orbits
harmonics
interactions

All Science Journal Classification (ASJC) codes

  • Physics and Astronomy(all)

Cite this

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title = "Soliton lattices in the Gross–Pitaevskii equation with nonlocal and repulsive coupling",
abstract = "Spatially-periodic patterns are studied in nonlocally coupled Gross–Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole–dipole interaction. Next, we study a model with a finite-range coupling, and show that a repulsively coupled system is closely related with an attractively coupled system and its soliton solution becomes a building block of the spatially-periodic structure. That is, the spatially-periodic structure can be interpreted as a soliton lattice. An approximate form of the soliton is given by a variational method. Furthermore, the effects of the rotating harmonic potential and spin-orbit coupling are numerically studied.",
author = "Hidetsugu Sakaguchi",
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N2 - Spatially-periodic patterns are studied in nonlocally coupled Gross–Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole–dipole interaction. Next, we study a model with a finite-range coupling, and show that a repulsively coupled system is closely related with an attractively coupled system and its soliton solution becomes a building block of the spatially-periodic structure. That is, the spatially-periodic structure can be interpreted as a soliton lattice. An approximate form of the soliton is given by a variational method. Furthermore, the effects of the rotating harmonic potential and spin-orbit coupling are numerically studied.

AB - Spatially-periodic patterns are studied in nonlocally coupled Gross–Pitaevskii equation. We show first that spatially periodic patterns appear in a model with the dipole–dipole interaction. Next, we study a model with a finite-range coupling, and show that a repulsively coupled system is closely related with an attractively coupled system and its soliton solution becomes a building block of the spatially-periodic structure. That is, the spatially-periodic structure can be interpreted as a soliton lattice. An approximate form of the soliton is given by a variational method. Furthermore, the effects of the rotating harmonic potential and spin-orbit coupling are numerically studied.

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