Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-New...Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.展开更多
With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element(1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hier...With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element(1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant γ to be determined. In the paper, we obtain a general formula for computing the constant γ. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions,the m Kd V equation and a generalized linear Kd V equation. The algebro-geometric solutions(also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced.展开更多
基金Supported by the Natural Science Foundation of China(Grant Nos.11547175,11271008)Supported by the Science and Technology Department of Henan Province(No.182102310978)Supported by the Aid Project for the Mainstay Young Teachers in Henan Provincial Institutions of Higher Education of China(Grant Nos.2017GGJS145,2014GGJS-195)
文摘Staring from a new spectral problem,a hierarchy of the generalized Kaup-Newell soliton equations is derived.By employing the trace identity their Hamiltonian structures are also generated.Then,the generalized Kaup-Newell soliton equations are decomposed into two systems of ordinary differential equations.The Abel-Jacobi coordinates are introduced to straighten the flows,from which the algebro-geometric solutions of the generalized KaupNewell soliton equations are obtained in terms of the Riemann theta functions.
基金Supported by the Innovation Team of Jiangsu Province hosted by China University of Mining and Technology(2014)the National Natural Science Foundation of China under Grant No.11371361+1 种基金the Fundamental Research Funds for the Central Universities(2013XK03)the Natural Science Foundation of Shandong Province under Grant No.ZR2013AL016
文摘With the help of a simple Lie algebra, an isospectral Lax pair, whose feature presents decomposition of element(1, 2) into a linear combination in the temporal Lax matrix, is introduced for which a new integrable hierarchy of evolution equations is obtained, whose Hamiltonian structure is also derived from the trace identity in which contains a constant γ to be determined. In the paper, we obtain a general formula for computing the constant γ. The reduced equations of the obtained hierarchy are the generalized nonlinear heat equation containing three-potential functions,the m Kd V equation and a generalized linear Kd V equation. The algebro-geometric solutions(also called finite band solutions) of the generalized nonlinear heat equation are obtained by the use of theory on algebraic curves. Finally, two kinds of gauge transformations of the spatial isospectral problem are produced.
