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

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

Yingnan Zhang^*, Yi He, Hon Wah Tam

^*Corresponding author for this work

Department of Computer Science

Research output: Contribution to journal › Journal article › peer-review

1 Citation (Scopus)

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.

Original language	English
Pages (from-to)	1085-1097
Number of pages	13
Journal	Frontiers of Mathematics in China
Volume	8
Issue number	5
DOIs	https://doi.org/10.1007/s11464-013-0308-8
Publication status	Published - Oct 2013

User-Defined Keywords

Bäcklund transformation (BT)
Integrability
nonlinear superposition formula
soliton solution

Access to Document

10.1007/s11464-013-0308-8

Cite this

@article{b2ee1473374b43c2bf40a0d18be28204,

title = "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 B{\"a}cklund transformation is derived and the corresponding nonlinear superposition formula is built.",

keywords = "B{\"a}cklund transformation (BT), Integrability, nonlinear superposition formula, soliton solution",

author = "Yingnan Zhang and Yi He and Tam, {Hon Wah}",

note = "Funding Information: Acknowledgements Y. Zhang and Y. He were grateful to Xingbiao Hu for helpful discussion. Y. He gratefully acknowledged the support of the K. C. Wong Education Foundation, Hong Kong, and her work was also partially supported by the National Natural Science Foundation of China (Grant No. 11201469) and the China Postdoctoral Science Foundation (Grant No. 2012M510186). This work was also partially supported by the Hong Kong Research Grant Council (Grant No. HKBU202512).",

year = "2013",

month = oct,

doi = "10.1007/s11464-013-0308-8",

language = "English",

volume = "8",

pages = "1085--1097",

journal = "Frontiers of Mathematics in China",

issn = "1673-3452",

publisher = "Higher Education Press Limited Company",

number = "5",

}

TY - JOUR

T1 - One variant of a (2 + 1)-dimensional Volterra system and its (1 + 1)-dimensional reduction

AU - Zhang, Yingnan

AU - He, Yi

AU - Tam, Hon Wah

N1 - Funding Information: Acknowledgements Y. Zhang and Y. He were grateful to Xingbiao Hu for helpful discussion. Y. He gratefully acknowledged the support of the K. C. Wong Education Foundation, Hong Kong, and her work was also partially supported by the National Natural Science Foundation of China (Grant No. 11201469) and the China Postdoctoral Science Foundation (Grant No. 2012M510186). This work was also partially supported by the Hong Kong Research Grant Council (Grant No. HKBU202512).

PY - 2013/10

Y1 - 2013/10

N2 - 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.

AB - 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.

KW - Bäcklund transformation (BT)

KW - Integrability

KW - nonlinear superposition formula

KW - soliton solution

UR - http://www.scopus.com/inward/record.url?scp=84882846092&partnerID=8YFLogxK

U2 - 10.1007/s11464-013-0308-8

DO - 10.1007/s11464-013-0308-8

M3 - Journal article

AN - SCOPUS:84882846092

SN - 1673-3452

VL - 8

SP - 1085

EP - 1097

JO - Frontiers of Mathematics in China

JF - Frontiers of Mathematics in China

IS - 5

ER -

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

Abstract

User-Defined Keywords

Access to Document

Other files and links

Fingerprint

Cite this