The -Matrix and an Algebraic-Geometric Solution of the AKNS System

Keywords

Integrable system, Mathematics, Matrix (chemical analysis), Algebraic number, Nonlinear system

References

• Tata Lectures on Theta IDavid Mumford — 1982
• Hamiltonian methods in the theory of solitonsL. D. Faddeev, Leon A. Takhtajan — 1987
• The Inverse scattering transform fourier analysis for nonlinear problemsMark J. Ablowitz, D. J. Kaup, Alan C. Newell — 1974
• Nonlinear-evolution equations of physical significanceMark J. Ablowitz, D. J. Kaup, Alan C. Newell — 1973
• r-matrix and algebraic-geometric solution for integrable symplectic mapZhijun Qiao — 1999
• Solitons and the Inverse Scattering TransformMark J. Ablowitz, Harvey Segur — 1981
• A Riemann-Hilbert approach to asymptotic problems arising in the theory of random matrix models, and also in the theory of integrable statistical mechanicsPercy Deift, Alexander Its, Xin Zhou — 1997
• Tata Lectures on Theta IDavid Mumford — 1983

Cited by

• The Application of Neumann Type Systems for Solving Integrable Nonlinear Evolution EquationsJinbing Chen — 2011
• Finite-gap solutions of 2+1 dimensional integrable nonlinear evolution equations generated by the Neumann systemsJinbing Chen — 2010
• Algebro-geometric Solutions for the Derivative Burgers HierarchyYu Hou, Engui Fan, Zhijun Qiao — 2015
• Some algebro-geometric solutions for the coupled modified Kadomtsev-Petviashvili equations arising from the Neumann type systemsJinbing Chen — 2012
• New finite-gap solutions for the coupled Burgers equations engendered by the Neumann systemsChen Jin-Bing, Geng Xian-Guo, Qiao Zhijun — 2010
• Dressed Dark Solitons of the Defocusing Nonlinear Schrödinger EquationSen‐Yue Lou, Xue-Ping Cheng, Xiaoyan Tang — 2014
• New Neumann System Associated with a 3 × 3 Matrix Spectral ProblemFang Li, Liping Lu — 2014
• Neumann type integrable reduction for nonlinear evolution equations in 1+1 and 2+1 dimensionsJinbing Chen — 2009
• Relation between the Negative-Order Harry Dym Hierarchy and a Family of Backward Neumann Type SystemsJinbing Chen — 2016
• Two kinds of finite-dimensional integrable reduction to the Harry-Dym hierarchyJinbing Chen — 2016

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