The full positive flows of Manakov hierarchy, Hamiltonian structures and conservation laws

作者: Lihua Wu , Guoliang He , Xianguo Geng

DOI: 10.1016/J.AMC.2013.05.050

关键词:

摘要: Based on four sets of Lenard recursion sequences and zero-curvature equation, we derive the full positive flows Manakov hierarchy associated with a 3x3 matrix spectral problem, from which some new nonlinear evolution equations are proposed. With help Darboux transformation, soliton solutions two in constructed. As special reductions, coupled modified Korteweg-de Vries Sasa-Satsuma deduced, included. And then, construct Hamiltonian structures infinite conservation laws several equations.

参考文章(59)
Abdul-Majid Wazwaz, Exact solutions for the fourth order nonlinear Schrodinger equations with cubic and power law nonlinearities Mathematical and Computer Modelling. ,vol. 43, pp. 802- 808 ,(2006) , 10.1016/J.MCM.2005.08.010
Miki Wadati, Takeshi Iizuka, Masato Hisakado, A Coupled Nonlinear Schrodinger Equation and Optical Solitons Journal of the Physical Society of Japan. ,vol. 61, pp. 2241- 2245 ,(1992) , 10.1143/JPSJ.61.2241
T. Kanna, M. Lakshmanan, P. Tchofo Dinda, Nail Akhmediev, Soliton collisions with shape change by intensity redistribution in mixed coupled nonlinear Schrödinger equations Physical Review E. ,vol. 73, pp. 026604- ,(2006) , 10.1103/PHYSREVE.73.026604
Abdullahi Rashid Adem, Chaudry Masood Khalique, On the solutions and conservation laws of a coupled KdV system Applied Mathematics and Computation. ,vol. 219, pp. 959- 969 ,(2012) , 10.1016/J.AMC.2012.06.076
J. Hurtubise, J. Hurtubise, J. Harnad, J. Harnad, M. R. Adams, Darboux coordinates and Liouville-Arnold integration in loop algebras Communications in Mathematical Physics. ,vol. 155, pp. 385- 413 ,(1993) , 10.1007/BF02097398
Narimasa Sasa, Junkichi Satsuma, New-Type of Soliton Solutions for a Higher-Order Nonlinear Schrödinger Equation Journal of the Physical Society of Japan. ,vol. 60, pp. 409- 417 ,(1991) , 10.1143/JPSJ.60.409
S. Mabrouk, M. Kassem, M. Abd-el-Malek, Group similarity solutions of the lax pair for a generalized Hirota-Satsuma equation Applied Mathematics and Computation. ,vol. 219, pp. 7882- 7890 ,(2013) , 10.1016/J.AMC.2013.02.013