Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity
We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes b...
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Veröffentlicht in: | Chaos (Woodbury, N.Y.) N.Y.), 2016-07, Vol.26 (7), p.073110-073110 |
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creator | Lebedev, M. E. Alfimov, G. L. Malomed, Boris A. |
description | We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too. |
doi_str_mv | 10.1063/1.4958710 |
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E. ; Alfimov, G. L. ; Malomed, Boris A.</creator><creatorcontrib>Lebedev, M. E. ; Alfimov, G. L. ; Malomed, Boris A.</creatorcontrib><description>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. 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L.</creatorcontrib><creatorcontrib>Malomed, Boris A.</creatorcontrib><title>Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity</title><title>Chaos (Woodbury, N.Y.)</title><addtitle>Chaos</addtitle><description>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.</description><subject>Bose-Einstein condensates</subject><subject>BOSE-EINSTEIN CONDENSATION</subject><subject>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</subject><subject>Cubic lattice</subject><subject>DIPOLES</subject><subject>Lattices (mathematics)</subject><subject>Mathematical analysis</subject><subject>MATHEMATICAL METHODS AND COMPUTING</subject><subject>Mathematical models</subject><subject>NONLINEAR OPTICS</subject><subject>NONLINEAR PROBLEMS</subject><subject>Nonlinearity</subject><subject>ONE-DIMENSIONAL CALCULATIONS</subject><subject>PERIODICITY</subject><subject>Schrodinger equation</subject><subject>SCHROEDINGER EQUATION</subject><subject>Solitary waves</subject><issn>1054-1500</issn><issn>1089-7682</issn><fulltext>true</fulltext><rsrctype>article</rsrctype><creationdate>2016</creationdate><recordtype>article</recordtype><recordid>eNp90U9vFCEYBvCJ0dh29eAXMCRe1GQqf4YBjqbRatLEQ3snLLzj0jAwBUbdxM_lF_CLOetuuyc9AcnvfQI8TfOC4HOCe_aOnHeKS0Hwo-aUYKla0Uv6eLfnXUs4xifNWSm3GGNCGX_anFDRCY4FPm1-XlezDoCcn9KylBR8TbEgE939Adk0TgF-QEE-oroBFFMMPoLJ6Npu8u9fzsevkBHczab6ZeC7rxs0QfbJeWtC2KIxuTmYCu446-v2WfNkMKHA88O6am4-fri5-NRefbn8fPH-qrWsI7VlSnIGHRkGZbk0SgIRwnCmuFVdx9aCCkGxBaqo4E66HoD3Cvdr1Q3OGbZqXu1jU6leF-sr2I1NMYKtmlKu-h6rRb3eqymnuxlK1aMvFkIwEdJcNJFYMtlz3h0DH-htmnNcnqApoURgxZdaVs2bvbI5lZJh0FP2o8lbTbDe9aaJPvS22JeHxHk9gnuQ90Ut4O0e7K7_95f_m_ZP_C3lI9STG9gfKlSv_Q</recordid><startdate>20160701</startdate><enddate>20160701</enddate><creator>Lebedev, M. 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L. ; Malomed, Boris A.</author></sort><facets><frbrtype>5</frbrtype><frbrgroupid>cdi_FETCH-LOGICAL-c341t-39853e41ff9c58a98e177a5395c9443b727720ce29275d8d6ee56906b94fdda3</frbrgroupid><rsrctype>articles</rsrctype><prefilter>articles</prefilter><language>eng</language><creationdate>2016</creationdate><topic>Bose-Einstein condensates</topic><topic>BOSE-EINSTEIN CONDENSATION</topic><topic>CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS</topic><topic>Cubic lattice</topic><topic>DIPOLES</topic><topic>Lattices (mathematics)</topic><topic>Mathematical analysis</topic><topic>MATHEMATICAL METHODS AND COMPUTING</topic><topic>Mathematical models</topic><topic>NONLINEAR OPTICS</topic><topic>NONLINEAR PROBLEMS</topic><topic>Nonlinearity</topic><topic>ONE-DIMENSIONAL CALCULATIONS</topic><topic>PERIODICITY</topic><topic>Schrodinger equation</topic><topic>SCHROEDINGER EQUATION</topic><topic>Solitary waves</topic><toplevel>peer_reviewed</toplevel><toplevel>online_resources</toplevel><creatorcontrib>Lebedev, M. E.</creatorcontrib><creatorcontrib>Alfimov, G. L.</creatorcontrib><creatorcontrib>Malomed, Boris A.</creatorcontrib><collection>PubMed</collection><collection>CrossRef</collection><collection>Technology Research Database</collection><collection>Aerospace Database</collection><collection>Advanced Technologies Database with Aerospace</collection><collection>MEDLINE - Academic</collection><collection>OSTI.GOV</collection><jtitle>Chaos (Woodbury, N.Y.)</jtitle></facets><delivery><delcategory>Remote Search Resource</delcategory><fulltext>fulltext</fulltext></delivery><addata><au>Lebedev, M. E.</au><au>Alfimov, G. L.</au><au>Malomed, Boris A.</au><format>journal</format><genre>article</genre><ristype>JOUR</ristype><atitle>Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity</atitle><jtitle>Chaos (Woodbury, N.Y.)</jtitle><addtitle>Chaos</addtitle><date>2016-07-01</date><risdate>2016</risdate><volume>26</volume><issue>7</issue><spage>073110</spage><epage>073110</epage><pages>073110-073110</pages><issn>1054-1500</issn><eissn>1089-7682</eissn><coden>CHAOEH</coden><abstract>We develop a general classification of the infinite number of families of solitons and soliton complexes in the one-dimensional Gross-Pitaevskii/nonlinear Schrödinger equation with a nonlinear lattice pseudopotential, i.e., periodically modulated coefficient in front of the cubic term, which takes both positive and negative local values. This model finds direct implementations in atomic Bose-Einstein condensates and nonlinear optics. The most essential finding is the existence of two branches of dipole solitons (DSs), which feature an antisymmetric shape, being essentially squeezed into a single cell of the nonlinear lattice. This soliton species was not previously considered in nonlinear lattices. We demonstrate that one branch of the DS family (namely, which obeys the Vakhitov-Kolokolov criterion) is stable, while unstable DSs spontaneously transform into stable fundamental solitons (FSs). The results are obtained in numerical and approximate analytical forms, the latter based on the variational approximation. Some stable bound states of FSs are found too.</abstract><cop>United States</cop><pub>American Institute of Physics</pub><pmid>27475070</pmid><doi>10.1063/1.4958710</doi><tpages>12</tpages><orcidid>https://orcid.org/0000-0001-5323-1847</orcidid></addata></record> |
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subjects | Bose-Einstein condensates BOSE-EINSTEIN CONDENSATION CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS Cubic lattice DIPOLES Lattices (mathematics) Mathematical analysis MATHEMATICAL METHODS AND COMPUTING Mathematical models NONLINEAR OPTICS NONLINEAR PROBLEMS Nonlinearity ONE-DIMENSIONAL CALCULATIONS PERIODICITY Schrodinger equation SCHROEDINGER EQUATION Solitary waves |
title | Stable dipole solitons and soliton complexes in the nonlinear Schrödinger equation with periodically modulated nonlinearity |
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