Algebro-geometric solutions to the Manakov hierarchy
作者： Lihua Wu , Xianguo Geng , Guoliang He
DOI: 10.1080/00036811.2015.1031220
关键词: Characteristic polynomial 、 Divisor (algebraic geometry) 、 Algebra 、 Function (mathematics) 、 Algebraic function 、 Mathematics 、 Theta function 、 Matrix (mathematics) 、 Hierarchy (mathematics) 、 Arithmetic genus
摘要: The Manakov hierarchy associated with a matrix spectral problem is proposed with the aid of Lenard recursion equations. By using the characteristic polynomial of Lax matrix for the …
sci-hub.se 参考文章(62)
V. I. Pulov, I. M. Uzunov, E. J. Chacarov, Solutions and laws of conservation for coupled nonlinear Schrodinger equations: Lie group analysis Physical Review E. ,vol. 57, pp. 3468- 3477 ,(1998) , 10.1103/PHYSREVE.57.3468
J. C. Eilbeck, V. Z. Enolskii, N. A. Kostov, Quasiperiodic and periodic solutions for vector nonlinear Schrödinger equations Journal of Mathematical Physics. ,vol. 41, pp. 8236- 8248 ,(2000) , 10.1063/1.1318733
R Sahadevan, K M Tamizhmani, M Lakshmanan, Painlevé analysis and integrability of coupled non-linear Schrödinger equations Journal of Physics A. ,vol. 19, pp. 1783- 1791 ,(1986) , 10.1088/0305-4470/19/10/019
B A Dubrovin, Theta functions and non-linear equations Russian Mathematical Surveys. ,vol. 36, pp. 11- 92 ,(1981) , 10.1070/RM1981V036N02ABEH002596
C. Menyuk, Nonlinear pulse propagation in birefringent optical fibers IEEE Journal of Quantum Electronics. ,vol. 23, pp. 174- 176 ,(1987) , 10.1109/JQE.1987.1073308
Y. Kodama, A.V. Mikhailov, Symmetry and perturbation of the vector nonlinear Schrödinger equation Physica D: Nonlinear Phenomena. ,vol. 152, pp. 171- 177 ,(2001) , 10.1016/S0167-2789(01)00168-3
Thambithurai Kanna, Eduard N. Tsoy, Nail Akhmediev, On the solution of multicomponent nonlinear Schrödinger equations Physics Letters A. ,vol. 330, pp. 224- 229 ,(2004) , 10.1016/J.PHYSLETA.2004.08.010
Claudia Valls, Quasiperiodic Solutions for Dissipative Boussinesq Systems Communications in Mathematical Physics. ,vol. 265, pp. 305- 331 ,(2006) , 10.1007/S00220-006-0026-0
R. DICKSON, F. GESZTESY, K. UNTERKOFLER, ALGEBRO-GEOMETRIC SOLUTIONS OF THE BOUSSINESQ HIERARCHY Reviews in Mathematical Physics. ,vol. 11, pp. 823- 879 ,(1999) , 10.1142/S0129055X9900026X
P. L. Christiansen, J. C.. Eilbeck, V. Z. Enolskii, N. A. Kostov, Quasi–periodic and periodic solutions for coupled nonlinear Schrödinger equations of Manakov type Proceedings of The Royal Society A: Mathematical, Physical and Engineering Sciences. ,vol. 456, pp. 2263- 2281 ,(2000) , 10.1098/RSPA.2000.0612