一个2+1维可积方程的代数几何解

Acta mathematica scientia,Series A ›› 2015, Vol. 35 ›› Issue (3): 534-544.

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Algebro-Geometric Solutions of A -Dimensional Integrable Equation

Chen Xiaohong^1,2, Zhang Daqing¹, Zhang Hongqing², You Fucai³

1 School of Science, University of Science and Technology LiaoNing, Liaoning Anshan 114051;
2 School of Mathematical Sciences, Dalian University of Technology, Liaoning Dalian 116024;
3 Department of Basic Sciences, Shenyang Institute of Engineering, Shenyang 110136

Received:2013-12-06 Revised:2014-10-21 Online:2015-06-25 Published:2015-06-25

Abstract

Abstract:

In this paper, a (2+1)-dimensional integrable equation is presented with the help of (1+1)-dimensional soliton equations. The (2+1)-dimensional integrable equation is decomposed into solvable ordinary differential equations. A hyperelliptic Riemann surface and Abel-Jacobi coordinates are introduced to strainghten the associated flow, from which the algebro-geometric solutions of the (2+1)-dimensional integrable equation are constructed by means of the Riemann theta functions.

Key words: Algebro-geometric solution, Abel-Jacobi coordinates, Riemann θ function

CLC Number:

O175.2

Chen Xiaohong, Zhang Daqing, Zhang Hongqing, You Fucai. Algebro-Geometric Solutions of A -Dimensional Integrable Equation[J].Acta mathematica scientia,Series A, 2015, 35(3): 534-544.

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References

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Algebro-Geometric Solutions of A -Dimensional Integrable Equation

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