Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential; Symmetry, Integrability and Geometry: Methods and Applications (SIGMA); Vol. 1
| Parent link: | Symmetry, Integrability and Geometry: Methods and Applications (SIGMA): Scientific Journal Vol. 1.— 2005.— [14 p.] |
|---|---|
| Autor Principal: | |
| Outros autores: | , |
| Summary: | Title screen The complex WKB–Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross–Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors. Although the WKB–Maslov method is approximate in essence, it leads to exact solution of the Gross–Pitaevskii equation with an external and a nonlocal quadratic potential. For this equation, an exact solution of the Cauchy problem is constructed in the class of trajectory concentrated functions. A nonlinear evolution operator is found in explicit form and symmetry operators (mapping a solution of the equation into another solution) are obtained for the equation under consideration. General constructions are illustrated by examples |
| Idioma: | inglés |
| Publicado: |
2005
|
| Subjects: | |
| Acceso en liña: | http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sigma&paperid=7&option_lang=rus |
| Formato: | MixedMaterials Electrónico Capítulo de libro |
| KOHA link: | https://koha.lib.tpu.ru/cgi-bin/koha/opac-detail.pl?biblionumber=636514 |
MARC
| LEADER | 00000nla0a2200000 4500 | ||
|---|---|---|---|
| 001 | 636514 | ||
| 005 | 20250328103845.0 | ||
| 035 | |a (RuTPU)RU\TPU\network\522 | ||
| 035 | |a RU\TPU\network\521 | ||
| 090 | |a 636514 | ||
| 100 | |a 20140210d2005 k||y0rusy50 ba | ||
| 101 | 0 | |a eng | |
| 102 | |a RU | ||
| 135 | |a drnn ---uucaa | ||
| 181 | 0 | |a i | |
| 182 | 0 | |a b | |
| 200 | 1 | |a Exact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential |f A. V. Shapovalov, A. Yu. Trifonov, A. L. Lisok | |
| 203 | |a Text |c electronic | ||
| 300 | |a Title screen | ||
| 320 | |a [References: 23 tit.] | ||
| 330 | |a The complex WKB–Maslov method is used to consider an approach to the semiclassical integrability of the multidimensional Gross–Pitaevskii equation with an external field and nonlocal nonlinearity previously developed by the authors. Although the WKB–Maslov method is approximate in essence, it leads to exact solution of the Gross–Pitaevskii equation with an external and a nonlocal quadratic potential. For this equation, an exact solution of the Cauchy problem is constructed in the class of trajectory concentrated functions. A nonlinear evolution operator is found in explicit form and symmetry operators (mapping a solution of the equation into another solution) are obtained for the equation under consideration. General constructions are illustrated by examples | ||
| 461 | |t Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) |o Scientific Journal | ||
| 463 | |t Vol. 1 |v [14 p.] |d 2005 | ||
| 610 | 1 | |a электронный ресурс | |
| 610 | 1 | |a труды учёных ТПУ | |
| 610 | 1 | |a WKB–Maslov complex germ method | |
| 610 | 1 | |a semiclassical asymptotics | |
| 610 | 1 | |a Gross–Pitaevskii equation | |
| 610 | 1 | |a solitons | |
| 610 | 1 | |a symmetry operators | |
| 700 | 1 | |a Shapovalov |b A. V. |c mathematician |c Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1949- |g Aleksandr Vasilyevich |3 (RuTPU)RU\TPU\pers\31734 | |
| 701 | 1 | |a Trifonov |b A. Yu. |c physicist, mathematician |c Professor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences |f 1963- |g Andrey Yurievich |3 (RuTPU)RU\TPU\pers\30754 | |
| 701 | 1 | |a Lisok |b A. L. |c physicist |c Associate Professor of Tomsk Polytechnic University, Candidate of physical and mathematical sciences |f 1981- |g Aleksandr Leonidovich |3 (RuTPU)RU\TPU\pers\31739 |9 15852 | |
| 801 | 2 | |a RU |b 63413507 |c 20180306 |g RCR | |
| 856 | 4 | |u http://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sigma&paperid=7&option_lang=rus | |
| 942 | |c CF | ||