The exact 
solutions of some
multicomponent integrable models

Yu. Yu. Berkela; Yu. M. Sidorenko

The exact solutions of multicomponent generalization of nonlinear Yajima-Oikawa model and their (2+1)-dimensional extensions are constructed in an explicit form. A vector Melnikov-like system has been integrated too.

1. Date E., Jimbo M., Kashiwara M., Miwa T. Nonlinear ntegrable systems: classical theory and quantum theory. Ed. Jimbo M. and Miwa T. – Singapore: World Scientific, 1983. – P. 39–119.

2. Dickey L.A. Soliton equations and Hamiltonian systems // Advanced Series in Mathematical Physics. – 1991. – V.12. – 310 p.

3. Sidorenko Yu., Strampp W. Symmetry constraints of the KP-hierarchy // Inverse Problems. – 1991. – V.7 – P.L-37–L-43.

4. Konopelchenko B., Sidorenko Yu., Strampp W. (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems // Phys. Lett. A. – 1991. – V.151. – P.17–21.

5. Sidorenko Yu. KP-hierachy and (1+1)-dimensional multicomponent integrable systems // Ukr. math. journ. – 1993. – V.25, № 1. – P.91–104.

6. Sidorenko Yu., Strampp W. Multicomponents integrable reductions in Kadomtsev-Petviashvilli hierarchy // J. Math. Phys. – 1993. – V.34, №.4. – P.1429–1446.

7. Oevel W., Strampp W. Constrained KP-hierarchy and bi-Hamiltonian structures // Commun. Math. Phys. – 1993. – V.157. – P.51–81.

8. Oevel W., Sidorenko Yu., Strampp W. Hamiltonian structures of the Melnicov system and its reductions // Inverse Problems. – 1993. – V.9. – P.737–747.

9. Samoilenko A.M., Samoilenko V.H., Sidorenko Yu.M. Hierarchy of equations Kadomtsev-Petviashvili with nonlocal constraints: Multidimensional generalizations and exact solutions of reduced systems /// Ukr. math. jour. – 1999. – V.51, № 1. – P.78–97.

10. Yajima N., Oikawa M. Formation and interaction of Sonic-Langmur solitons: inverse scattering method // Progress Theoret. Phys. – 1976. – V.56, № 6. – P.1719–1739.

11. Cидоренко Ю.M. Метод інтегрування рівнянь Лакса з нелокальними редукціями // Доп. НАН України. – 1999. – № 9. – P.33–36.

12. Takhtadzhan L.A., Faddeev L.D. Hamiltonian method in the theory of solitons. Springer, Berlin. – 1987.

13. Melnikov V.K. On equations integrable by the inverse scattering method. – Preprint No. P2-85-958. Joint institute for nuclear research, Dubna. – 1985.

	The exact solutions of some multicomponent integrable models
Author	Yu. Yu. Berkela, Yu. M. Sidorenko matmod@franko.lviv.ua Faculty of Mechanics and Mathematics, Lviv National University
Abstract	The exact solutions of multicomponent generalization of nonlinear Yajima-Oikawa model and their (2+1)-dimensional extensions are constructed in an explicit form. A vector Melnikov-like system has been integrated too.
Keywords	exact solutions, multicomponent generalization, nonlinear Yajima-Oikawa model, explicit form, vector Melnikov-like system
DOI	doi:10.30970/ms.17.1.47-58
Reference	1. Date E., Jimbo M., Kashiwara M., Miwa T. Nonlinear ntegrable systems: classical theory and quantum theory. Ed. Jimbo M. and Miwa T. – Singapore: World Scientific, 1983. – P. 39–119. 2. Dickey L.A. Soliton equations and Hamiltonian systems // Advanced Series in Mathematical Physics. – 1991. – V.12. – 310 p. 3. Sidorenko Yu., Strampp W. Symmetry constraints of the KP-hierarchy // Inverse Problems. – 1991. – V.7 – P.L-37–L-43. 4. Konopelchenko B., Sidorenko Yu., Strampp W. (1+1)-dimensional integrable systems as symmetry constraints of (2+1)-dimensional systems // Phys. Lett. A. – 1991. – V.151. – P.17–21. 5. Sidorenko Yu. KP-hierachy and (1+1)-dimensional multicomponent integrable systems // Ukr. math. journ. – 1993. – V.25, № 1. – P.91–104. 6. Sidorenko Yu., Strampp W. Multicomponents integrable reductions in Kadomtsev-Petviashvilli hierarchy // J. Math. Phys. – 1993. – V.34, №.4. – P.1429–1446. 7. Oevel W., Strampp W. Constrained KP-hierarchy and bi-Hamiltonian structures // Commun. Math. Phys. – 1993. – V.157. – P.51–81. 8. Oevel W., Sidorenko Yu., Strampp W. Hamiltonian structures of the Melnicov system and its reductions // Inverse Problems. – 1993. – V.9. – P.737–747. 9. Samoilenko A.M., Samoilenko V.H., Sidorenko Yu.M. Hierarchy of equations Kadomtsev-Petviashvili with nonlocal constraints: Multidimensional generalizations and exact solutions of reduced systems /// Ukr. math. jour. – 1999. – V.51, № 1. – P.78–97. 10. Yajima N., Oikawa M. Formation and interaction of Sonic-Langmur solitons: inverse scattering method // Progress Theoret. Phys. – 1976. – V.56, № 6. – P.1719–1739. 11. Cидоренко Ю.M. Метод інтегрування рівнянь Лакса з нелокальними редукціями // Доп. НАН України. – 1999. – № 9. – P.33–36. 12. Takhtadzhan L.A., Faddeev L.D. Hamiltonian method in the theory of solitons. Springer, Berlin. – 1987. 13. Melnikov V.K. On equations integrable by the inverse scattering method. – Preprint No. P2-85-958. Joint institute for nuclear research, Dubna. – 1985.
Pages	47-58
Volume	17
Issue	1
Year	2002
Journal	Matematychni Studii
Full text of paper	pdf
Table of content of issue	html

The exact solutions of some multicomponent integrable models