After the (1 + 1)-dimensional nonlinear Schrodinger equation is embedded in higher dimensions and the usual singularity analysis approach is extended such that all the Painleve expansion coefficients are conformal inv...After the (1 + 1)-dimensional nonlinear Schrodinger equation is embedded in higher dimensions and the usual singularity analysis approach is extended such that all the Painleve expansion coefficients are conformal invariant, many higher dimensional integrable models are got after the nontrivial conformal invariant expansion coefficients are taken to be zero simply. The Painleve properties of the obtained higher dimensional models (including some (3 + 1)-dimensional models) are proved.展开更多
We analyse the integrable boundary conditions for the one-dimensional N-component generalized Bariev model with a hard-core repulsion. The Bethe ansatz equations and the energy spectrum are obtained in the framework o...We analyse the integrable boundary conditions for the one-dimensional N-component generalized Bariev model with a hard-core repulsion. The Bethe ansatz equations and the energy spectrum are obtained in the framework of the nested Bethe ansatz method.展开更多
Using Sklyanin's formalism, the authors study two integrable nineteen-vertex models with open boundary conditions(BC). By solving reflection equation(RE), three different diagonal boundary K matrices for each mode...Using Sklyanin's formalism, the authors study two integrable nineteen-vertex models with open boundary conditions(BC). By solving reflection equation(RE), three different diagonal boundary K matrices for each model are obtained and the corresponding explicit forms of the Hamiltonians with three different kinds of nontrival boundary terms are given.展开更多
In general, Liouville integrable hierarchies of evolution equations were obtained by choosing proper U in zero curvature frame Ut - Vx + [U, V] = 0 first. But in the present paper, a new Liouville integrable hierarchy...In general, Liouville integrable hierarchies of evolution equations were obtained by choosing proper U in zero curvature frame Ut - Vx + [U, V] = 0 first. But in the present paper, a new Liouville integrable hierarchy possessing bi-Hamiltonian structure is obtained by choosing V with derivatives in x and spectral potentials. Then integrable coupling, i.e. expanding Lax integrable model of the hierarchy obtained is presented by constructing a subalgebra of loop algebra A2.展开更多
Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coeffi...Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.展开更多
The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painle...The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.展开更多
A direct method for obtaining the expanding integrable models of the hierarchies of evolution equations was proposed. By using the equivalent transformation between the matrices, a new isospectral problem was directly...A direct method for obtaining the expanding integrable models of the hierarchies of evolution equations was proposed. By using the equivalent transformation between the matrices, a new isospectral problem was directly established according to the known isospectral problem, which can be used to obtain the expanding integrable model of the known hierarchy.展开更多
Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantu...Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantum model is relevant to Lee model.展开更多
基金Project supported by the National Natural Science Foundation of China (Grant No. 19975025) National "Climbing Project", Natural Science Foundation of Zhejiang Province Youth Foundation of Zhejiang Province
文摘After the (1 + 1)-dimensional nonlinear Schrodinger equation is embedded in higher dimensions and the usual singularity analysis approach is extended such that all the Painleve expansion coefficients are conformal invariant, many higher dimensional integrable models are got after the nontrivial conformal invariant expansion coefficients are taken to be zero simply. The Painleve properties of the obtained higher dimensional models (including some (3 + 1)-dimensional models) are proved.
基金Supported by the National Natural Science Foundation of China under Grant No 90103001,
文摘We analyse the integrable boundary conditions for the one-dimensional N-component generalized Bariev model with a hard-core repulsion. The Bethe ansatz equations and the energy spectrum are obtained in the framework of the nested Bethe ansatz method.
文摘Using Sklyanin's formalism, the authors study two integrable nineteen-vertex models with open boundary conditions(BC). By solving reflection equation(RE), three different diagonal boundary K matrices for each model are obtained and the corresponding explicit forms of the Hamiltonians with three different kinds of nontrival boundary terms are given.
文摘In general, Liouville integrable hierarchies of evolution equations were obtained by choosing proper U in zero curvature frame Ut - Vx + [U, V] = 0 first. But in the present paper, a new Liouville integrable hierarchy possessing bi-Hamiltonian structure is obtained by choosing V with derivatives in x and spectral potentials. Then integrable coupling, i.e. expanding Lax integrable model of the hierarchy obtained is presented by constructing a subalgebra of loop algebra A2.
基金Project supported by the National Natural Science Foundation of China.
文摘Starting from the similarity reductions of the Kadomtsev-Petviashvili equation, we getthe generalized Boussinesq equation and the generalized KdV equation which possess somearbitrary functions as their variable coefficients. Using the singularity analysis methoddeveloped by J. Weiss and M. D. Kruskal et al. we have proved the sufficient conditionsof the integrabilities and Painleve properties of these two equations. Their Backlund trans-formations and the singularity manifold equations (generalized Schwartz-Boussinesq equationand Schwartz-KdV equation) are obtained. And then these two equations are linearized, i. e.their Lax pairs are given with the time-independent arbitrary spectral parameters includedexplicitly.
基金supported by the National Natural Science Foundation of China (Grant No 10575087)the Natural Science Foundation of Zhejiang Province,China (Grant No 102053)
文摘The usual （1＋1）-dimensional Schwartz Boussinesq equation is extended to the （1＋1）-dimensional space-time symmetric form and the general （n＋1）-dimensional space-time symmetric form. These extensions are Painleve integrable in the sense that they possess the Painleve property. The single soliton solutions and the periodic travelling wave solutions for arbitrary dimensional space-time symmetric form are obtained by the Painleve-Backlund transformation.
基金Project supported by the National Natural Science Foundation of China （Grant Nos.10371070, 10547123）
文摘A direct method for obtaining the expanding integrable models of the hierarchies of evolution equations was proposed. By using the equivalent transformation between the matrices, a new isospectral problem was directly established according to the known isospectral problem, which can be used to obtain the expanding integrable model of the known hierarchy.
文摘Ⅰ. INTRODUCTION The model of three-wave interaction plays an important role in plasma physics and nonlinear optics. Its classical cases and quantum cases have been studied by many authors. As shown in [4], the quantum model is relevant to Lee model.
