Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy

Volume 9, Issue 2, pp 661--676 http://dx.doi.org/10.22436/jnsa.009.02.29

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Authors

Qian Li - Department of Mathematics, Shanghai University, Shanghai, 200444, China. Tiecheng Xia - Department of Mathematics, Shanghai University, Shanghai, 200444, China. Chao Yue - College of Information Engineering, Taishan Medical University, Taian, 271016, China.

Abstract

This paper is dedicated to provide explicit theta function representation of algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy. Our main tools include zero-curvature equation to derive the generalized nonlinear Schrödinger hierarchy, the hyper-elliptic curve with genus of N, the Abel-Jacobi coordinates, the meromorphic function, the Baker-Akhiezer functions, and the Dubrovin-type equations for auxiliary divisors. With the help of these tools, the explicit representations of the Baker-Ahhiezer functions, the meromorphic function, and the algebro-geometric solutions are obtained for the whole generalized nonlinear Schrödinger hierarchy.

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Keywords

• Algebro-geometric solutions
• Abel-Jacobi coordinates
• meromorphic function
• Dubrovin-type equations
• generalized nonlinear Schrödinger hierarchy.

MSC

•  37K10
•  58F07
•  35Q35

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