广义Broer-Kaup-Kupershmidt孤子方程的拟周期解

Acta mathematica scientia,Series A ›› 2016, Vol. 36 ›› Issue (2): 317-327.

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Quasi-Periodic Solution of the Generalized Broer-Kaup-Kupershmidt Soliton Equation

Wei Hanyu¹, Xia Tiecheng²

1 College of Mathematics and Statistics, Zhoukou Normal University, Henan Zhoukou 466001;
2 Department of Mathematics, Shanghai University, Shanghai 200444

Received:2015-09-06 Revised:2016-01-03 Online:2016-04-25 Published:2016-04-25
Supported by:
Supported by the NSFC (11271008, 61072147, 11547175, 11447220), the First-class Discipline of University in Shanghai, the Science and Technology Department of Henan Province (152300410230), the Key Scientific Research Projects of Henan Province (16A110026) and the Doctoral Research Fundation of Zhoukou Normal University (ZKNU2014130)

Abstract

Abstract:

In this paper, starting from a new spectral problem, a new (2+1)-dimensional generalized Broer-Kaup-Kupershmidt soliton equation is decomposed into systems of integrable ordinary differential equations resorting to the nonlinearization of Lax pairs. Then, 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 solution of the (2+1)-dimensional generalized Broer-Kaup-Kupershmidt soliton equation is obtained in terms of Riemann theta functions.

Key words: Nonlinearization, Abel-Jacobi coordinates, Riemann theta function, Quasi-periodic solution

CLC Number:

O175.29

Wei Hanyu, Xia Tiecheng. Quasi-Periodic Solution of the Generalized Broer-Kaup-Kupershmidt Soliton Equation[J].Acta mathematica scientia,Series A, 2016, 36(2): 317-327.

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Quasi-Periodic Solution of the Generalized Broer-Kaup-Kupershmidt Soliton Equation

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