Quasi-periodic solution of the (2+1)-dimensional Boussinesq-Burgers soliton equation

Jinshun Zhang; Yongtang Wu; Xuemei Li

doi:10.1016/S0378-4371(02)01526-1

Quasi-periodic solution of the (2+1)-dimensional Boussinesq-Burgers soliton equation

Jinshun Zhang^*, Yongtang Wu, Xuemei Li

^*Corresponding author for this work

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

20 Citations (Scopus)

Abstract

A (2+1)-dimensional Bossinesq-Burgers soliton equation is proposed, which has a affinitive connection with the Boussinesq-Burgers soliton hierarchy. Through a natural nonlinearization of the Boussinesq-Burgers's eigenvalue problems, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the (2+1)-dimensional Boussinesq-Burgers equation are derived by resorting to the Riemann theta functions.

Original language	English
Pages (from-to)	213-232
Number of pages	20
Journal	Physica A: Statistical Mechanics and its Applications
Volume	319
Early online date	23 Oct 2002
DOIs	https://doi.org/10.1016/S0378-4371(02)01526-1
Publication status	Published - 1 Mar 2003
Externally published	Yes

User-Defined Keywords

Abel-Jacobi coordinates
Integrable systems
Theta functions

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10.1016/S0378-4371(02)01526-1

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title = "Quasi-periodic solution of the (2+1)-dimensional Boussinesq-Burgers soliton equation",

abstract = "A (2+1)-dimensional Bossinesq-Burgers soliton equation is proposed, which has a affinitive connection with the Boussinesq-Burgers soliton hierarchy. Through a natural nonlinearization of the Boussinesq-Burgers's eigenvalue problems, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the (2+1)-dimensional Boussinesq-Burgers equation are derived by resorting to the Riemann theta functions.",

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author = "Jinshun Zhang and Yongtang Wu and Xuemei Li",

note = "Funding Information: This work was partially supported by Hong Kong RGC:HKBU 2043/00p. Project 10071075 was supported by National Natural Science Foundation of China. One of the authors (JSZ) would like to thank the Henan Science Foundation Committee of China for financial support. Publisher copyright: {\textcopyright} 2002 Elsevier Science B.V. All rights reserved.",

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AU - Zhang, Jinshun

AU - Wu, Yongtang

AU - Li, Xuemei

N1 - Funding Information: This work was partially supported by Hong Kong RGC:HKBU 2043/00p. Project 10071075 was supported by National Natural Science Foundation of China. One of the authors (JSZ) would like to thank the Henan Science Foundation Committee of China for financial support. Publisher copyright: © 2002 Elsevier Science B.V. All rights reserved.

PY - 2003/3/1

Y1 - 2003/3/1

N2 - A (2+1)-dimensional Bossinesq-Burgers soliton equation is proposed, which has a affinitive connection with the Boussinesq-Burgers soliton hierarchy. Through a natural nonlinearization of the Boussinesq-Burgers's eigenvalue problems, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the (2+1)-dimensional Boussinesq-Burgers equation are derived by resorting to the Riemann theta functions.

AB - A (2+1)-dimensional Bossinesq-Burgers soliton equation is proposed, which has a affinitive connection with the Boussinesq-Burgers soliton hierarchy. Through a natural nonlinearization of the Boussinesq-Burgers's eigenvalue problems, a finite-dimensional Hamiltonian system is obtained and is proved to be completely integrable in Liouville sense. The Abel-Jacobi coordinates are constructed to straighten out the Hamiltonian flows, from which the quasi-periodic solutions of the (2+1)-dimensional Boussinesq-Burgers equation are derived by resorting to the Riemann theta functions.

KW - Abel-Jacobi coordinates

KW - Integrable systems

KW - Theta functions

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U2 - 10.1016/S0378-4371(02)01526-1

DO - 10.1016/S0378-4371(02)01526-1

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SN - 0378-4371

VL - 319

SP - 213

EP - 232

JO - Physica A: Statistical Mechanics and its Applications

JF - Physica A: Statistical Mechanics and its Applications

ER -

Quasi-periodic solution of the (2+1)-dimensional Boussinesq-Burgers soliton equation

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