Algebro-geometric solutions for the generalized nonlinear Schrödinger hierarchy

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作者单位: College of Information Engineering, Taishan Medical University, Taian, 271016, China a Department of Mathematics, Shanghai University, Shanghai, 200444, China

关键词: Abel-Jacobi coordinates Algebro-geometric solutions Dubrovin-type equations Generalized nonlinear Schrödinger hierarchy Meromorphic function

摘要: 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 representa...更多; 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.收起

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