A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Da...A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations. The exact solutions are given by applying the Darboux transformation.展开更多
A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of c...A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy.展开更多
This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructe...This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.展开更多
A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely...A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.展开更多
A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discr...A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.展开更多
Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the n...Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Backlund transformation for such a coupled system denoting in the F functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.展开更多
基金Supported by the National Natural Science Foundation of China under Grant No.10771207
文摘A hierarchy of nonlinear lattice soliton equations is derived from a new discrete spectral problem. The Hamiltonian structure of the resulting hierarchy is constructed by using a trace identity formula. Moreover, a Darboux transformation is established with the help of gauge transformations of Lax pairs for the typical lattice soliton equations. The exact solutions are given by applying the Darboux transformation.
基金Project supported by National Natural Science Fundation of China(Grant No .10371070)
文摘A discrete isospectral problem and the associated hierarchy of Lax integrable lattice equations were investigated. A Darboux transformation for the discrete spectral problem was found. Finally, an infinite number of conservation laws were given for the corresponding hierarchy.
基金supported by the National Natural Science Foundation of China (Grant No.11505090)Liaocheng University Level Science and Technology Research Fund (Grant No.318012018)+2 种基金Discipline with Strong Characteristics of Liaocheng University–Intelligent Science and Technology (Grant No.319462208)Research Award Foundation for Outstanding Young Scientists of Shandong Province (Grant No.BS2015SF009)the Doctoral Foundation of Liaocheng University (Grant No.318051413)。
文摘This article presents the construction of a nonlocal Hirota equation with variable coefficients and its Darboux transformation.Using zero-seed solutions,1-soliton and 2-soliton solutions of the equation are constructed through the Darboux transformation,along with the expression for N-soliton solutions.Influence of coefficients that are taken as a function of time instead of a constant,i.e.,coefficient functionδ(t),on the solutions is investigated by choosing the coefficient functionδ(t),and the dynamics of the solutions are analyzed.This article utilizes the Lax pair to construct infinite conservation laws and extends it to nonlocal equations.The study of infinite conservation laws for nonlocal equations holds significant implications for the integrability of nonlocal equations.
基金Supported by National Natural Science Foundation of China under Grant Nos.11171312 and 11126308Science and Technology Research Key Projects of the Education Department of Henan Province under Grant No.12A110023
文摘A hierarchy of new nonlinear evolution equations associated with a 2 x 2 matrix spectral problem is derived. One of the nontrivial equations in this hierarchy is the famous Sharma-Tasso-Olver equation. Then infinitely many conservation laws of this equation are deduced. Darboux transformation for the Sharma-Tasso-Olver equation is constructed with the aid of a gauge transformation.
基金The project supported by the Scientific Research Award Foundation for Outstanding Young and Middle-Aged Scientists of Shandong Province of China
文摘A discrete matrix spectral problem and the associated hierarchy of Lax integrable lattice equations are presented, and it is shown that the resulting Lax integrable lattice equations are all Liouville integrable discrete Hamiltonian systems. A new integrable symplectic map is given by binary Bargmann constraint of the resulting hierarchy. Finally, an infinite set of conservation laws is given for the resulting hierarchy.
基金Supported by the Foundation of Beijing Information Science and Technology University (Grant No. 1025020)Scientific Research Project of Beijing Educational Committee (Grant No. SQKM201211232016)+3 种基金Natural Science Foundation of Beijing (Grant No. 1102018)National Natural Science Foundation of China (Grant No. 61072145)Key Project of Chinese Ministry of Education (Grant No. 106033)National Basic Research Program of China (973 Program) (Grant No. 2005CB321901)
文摘Considering the integrable properties for the coupled equations, the variable-coefficient N- coupled nonlinear Schrodinger equations are under investigation analytically in this paper. Based on the Lax pair with the nonisospectral parameter, a Backlund transformation for such a coupled system denoting in the F functions is constructed with the one-solitonic solution given as the application sample. Furthermore, an infinite number of conservation laws are obtained using symbolic computation.
