Integration of nonlinear space-twodimensional Heisenberg equations (in Ukrainian) |
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| Author |
Ivan Franko National University of Lviv, Faculty of Mechanics and Mathematics
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| Abstract |
We investigate the model of Ishimori I (nonlinear (2+1)-dimensional generalizations
of Heisenberg equations) and its modification.
For these systems the method
of constructing of a wide class of exact solutions in explicit form is proposed
by using of ``dressing" transformations of Zakharov-Shabat type.
As particular cases we present solutions which
are essentially different from already known.
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| Keywords |
model of Ishimori I, dimensional generalizations of Heisenberg equations, explicit form, dressing transformations of Zakharov-Shabat type
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| DOI |
doi:10.30970/ms.18.1.57-68
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Reference |
1. Ishimori Y. Multi-vortex solutions of a two-dimensional nonlinear wave equation // Progr. Theor. Rhys.– 1983. – V.72, № 1. - С.33-39.
2. Konopelchenko B. G. Solitons in multidimensions. Singapore: WorldScientific, 1993 3. Беркела Ю., Сидоренко Ю. Нелінійна модель типу Ўшиморі як редукція некононічної іїрархії Кадомцева-Петвіашвілі // Вісник Львів. унів. Сер. мех.-мат. – 2001. – Вип.59. – C.74–83. 4. Imai K. Dromion and lump solutions of the Ishimori-I equation // Progress of Theor. Physics. – 1997. – V. 98, № 5. – P. 1013-1023. 5. Imai K., Nozaki K. (2+1)-Dimensional soliton equations covariant with respect to the binary Darboux transformation // Journ. of the Phys. Society of Japan. – 1996. – V. 65, № 1. – P. 53–57. 6. Konopelchenko B. G., Oevel W. Matrix Sato theory and integrable equations in 2+1 dimensions // Proceedings of the 7th Workshop on Nonlinear Evolution Equations and Dynamical systems (NEEDS'91), Biala Verda, Italy, 19-29 June 1991. 7. Сидоренко Ю. М. Матричне узагальнення іїрархії Кадомцева – Петвіашвілі і нелінійні інтегровні системи // Нелінійні коливання. – 1999. – Вип.2. – № 2. – C.30–39. 8. Sidorenko Yu. Transformation operators for integrable hierarchies with additional reductions // Proceedings of Institute of Math. of NAS of Ukraine. – 2002.– V.43, Part 1. – P. 352-357. |
| Pages |
57-68
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| Volume |
18
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| Issue |
1
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| Year |
2002
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| Journal |
Matematychni Studii
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| Full text of paper | |
| Table of content of issue |