One variant of a (2+ 1)-dimensional Volterra system and its (1+ 1)-dimensional reduction

Abstract

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.

Keywords

Integrability / soliton solution / Bäcklund transformation (BT) / nonlinear superposition formula

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