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

Yingnan Zhang; Yi He; Hon-Wah Tam

doi:10.1007/s11464-013-0308-8

Front. Math. China ›› 2013, Vol. 8 ›› Issue (5) : 1085 -1097. DOI: 10.1007/s11464-013-0308-8

Research Article

RESEARCH ARTICLE

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

Yingnan Zhang ¹^,²^,^a
, Yi He ³
, Hon-Wah Tam ⁴

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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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Yingnan Zhang, Yi He, Hon-Wah Tam. One variant of a (2 + 1)-dimensional Volterra system and its (1 + 1)-dimensional reduction. Front. Math. China, 2013, 8(5): 1085-1097 DOI:10.1007/s11464-013-0308-8

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