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| 005 | 20231030040137.0 | ||
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| 100 | _a20140210a2005 k y0engy50 ba | ||
| 101 | 0 | _aeng | |
| 102 | _aRU | ||
| 135 | _adrnn ---uucaa | ||
| 181 | 0 | _ai | |
| 182 | 0 | _ab | |
| 200 | 1 |
_aExact Solutions and Symmetry Operators for the Nonlocal Gross-Pitaevskii Equation with Quadratic Potential _fA. V. Shapovalov, A. Yu. Trifonov, A. L. Lisok |
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| 203 |
_aText _celectronic |
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| 300 | _aTitle screen | ||
| 320 | _a[References: 23 tit.] | ||
| 330 | _aThe 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 |
_tSymmetry, Integrability and Geometry: Methods and Applications (SIGMA) _oScientific Journal |
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| 463 |
_tVol. 1 _v[14 p.] _d2005 |
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| 610 | 1 | _aэлектронный ресурс | |
| 610 | 1 | _aтруды учёных ТПУ | |
| 610 | 1 | _aWKB–Maslov complex germ method | |
| 610 | 1 | _asemiclassical asymptotics | |
| 610 | 1 | _aGross–Pitaevskii equation | |
| 610 | 1 | _asolitons | |
| 610 | 1 | _asymmetry operators | |
| 700 | 1 |
_aShapovalov _bA. V. _cmathematician _cProfessor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1949- _gAleksandr Vasilyevich _2stltpush _3(RuTPU)RU\TPU\pers\31734 |
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| 701 | 1 |
_aTrifonov _bA. Yu. _cphysicist, mathematician _cProfessor of Tomsk Polytechnic University, Doctor of physical and mathematical sciences _f1963- _gAndrey Yurievich _2stltpush _3(RuTPU)RU\TPU\pers\30754 |
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| 701 | 1 |
_aLisok _bA. L. _cphysicist _cAssociate Professor of Tomsk Polytechnic University, Candidate of physical and mathematical sciences _f1981- _gAleksandr Leonidovich _2stltpush _3(RuTPU)RU\TPU\pers\31739 |
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| 801 | 2 |
_aRU _b63413507 _c20180306 _gRCR |
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| 856 | 4 | _uhttp://www.mathnet.ru/php/archive.phtml?wshow=paper&jrnid=sigma&paperid=7&option_lang=rus | |
| 942 | _cCF | ||