Hamiltonian Structures and Integrability for a Discrete Coupled KdV-Type Equation Hierarchy

Coupled Korteweg-de Vries (KdV) systems have many important physical applications. By considering a 4 × 4 spectral problem, we derive a discrete coupled KdV-type equation hierarchy. Our hierarchy includes the coupled Volterra system proposed by Lou et al. (e-print arXiv:0711.0420) as the first member which is a discrete version of the coupled KdV equation. We also investigate the integrability in the Liouville sense and the multi-Hamiltonian structures for the obtained hierarchy.

[1]  Zuo-nong Zhu,et al.  Multisoliton, multipositon, multinegaton, and multiperiodic solutions of a coupled Volterra lattice system and their continuous limits , 2011 .

[2]  Lou Sen-yue,et al.  Lie Point Symmetries and Exact Solutions of the Coupled Volterra System , 2010 .

[3]  R. Sahadevan,et al.  Similarity reduction, generalized symmetries, recursion operator, and integrability of coupled Volterra system , 2008 .

[4]  M. Wadati,et al.  Wave Propagations in the F=1 Spinor Bose-Einstein Condensates(Atomic and Molecular Physics) , 2006 .

[5]  Xiao-yan Tang,et al.  Coupled KdV equations derived from two-layer fluids , 2005, nlin/0508029.

[6]  WadatiMiki,et al.  Wave Propagations in the F=1 Spinor Bose–Einstein Condensates , 2005 .

[7]  V. Konotop,et al.  Stable and unstable vector dark solitons of coupled nonlinear Schrödinger equations: application to two-component Bose-Einstein condensates. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Mikhail V. Foursov,et al.  On integrable coupled KdV-type systems , 2000 .

[9]  S. I. Svinolupov,et al.  Integrable boundary value problems for the multicomponent Schro¨dinger equations , 1995 .

[10]  S. I. Svinolupov.  Generalized Schrödinger equations and Jordan pairs , 1992 .

[11]  T Gui-zhang,et al.  A trace identity and its applications to the theory of discrete integrable systems , 1990 .

[12]  J. Gear.  Strong Interactions between Solitary Waves Belonging to Different Wave Modes , 1985 .

[13]  Ryogo Hirota,et al.  A coupled KdV equation is one case of the four-reduction of the KP hierarchy , 1982 .

[14]  Masaaki Ito,et al.  Symmetries and conservation laws of a coupled nonlinear wave equation , 1982 .

[15]  Allan P. Fordy,et al.  On the integrability of a system of coupled KdV equations , 1982 .

[16]  R. Hirota,et al.  Soliton solutions of a coupled Korteweg-de Vries equation , 1981 .