Department of Computer Science
One variant of a (2 + 1)-dimensional Volterra system and its (1 + 1)-dimensional reduction
A new system is generated from a multi-linear form of a (2+1)-dimensional Volterra system. Though the system is only partially integrable and needs additional conditions to possess two-soliton solutions, its (1+1)-dimensional reduction gives an integrable equation which has been studied via reduction skills. Here, we give this (1+1)-dimensional reduction a simple bilinear form, from which a Bäcklund transformation is derived and the corresponding nonlinear superposition formula is built. © 2013 Higher Education Press and Springer-Verlag Berlin Heidelberg.
Bäcklund transformation (BT), Integrability, nonlinear superposition formula, soliton solution
Source Publication Title
Frontiers of Mathematics in China
Zhang, Yingnan, Yi He, and Hon-Wah Tam. "One variant of a (2 + 1)-dimensional Volterra system and its (1 + 1)-dimensional reduction." Frontiers of Mathematics in China 8.5 (2013): 1085-1097.