Mukherjee-Choudhury-Chowdhury spectral problem and the semi-discrete integrable system

作者：Xu, Xi-Xiang^*; Sun, Ye-Peng

来源：International Journal of Modern Physics B, 2016, 30(28-29): 1640027.

DOI：10.1142/S0217979216400270

• Semi-discrete integrable system
• Backlund transformation of Darboux type
• Lax pair
• involutive representation of solution

Starting from the Mukherjee Choudhury Chowdhury spectral problem, we derive a semi-discrete integrable system by a proper time spectral problem. A Backlund transformation of Darboux type of this system is established with the help of gauge transformation of the Lax pairs. By means of the obtained Backlund transformation, an exact solution is given. Moreover, Hamiltonian form of this system is constructed. Further, through a constraint of potentials and eigenfunctions, the Lax pair and the adjoint Lax pair of the obtained semi-discrete integrable system are nonlinearized as an integrable symplectic map and a completely integrable finite-dimensional Hamiltonian system in the Liouville sense. Finally, the involutive representation of solution of the obtained semi-discrete integrable system is presented.

• 出版日期2016-11-20
• 单位山东财经大学; 山东科技大学