We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and the...We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.展开更多
On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in...On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel-Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.展开更多
This paper considers classical strings propagating in γ-deformed AdS3 γ S^3 backgrounds generated by certain shift T-dualities accompanied （TsT） transformations on S^3 and AdS3, respectively. It finds that the U（...This paper considers classical strings propagating in γ-deformed AdS3 γ S^3 backgrounds generated by certain shift T-dualities accompanied （TsT） transformations on S^3 and AdS3, respectively. It finds that the U（1） currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds generated by TsT transformations on both S3 and ADS3. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in γ-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.展开更多
Finite-dimensional integrable Hamiltonian system, obtained through the nonlinearization of the 3 × 3 spectral problem associated with the Boussinesq equation, is investigated. A generating function method startin...Finite-dimensional integrable Hamiltonian system, obtained through the nonlinearization of the 3 × 3 spectral problem associated with the Boussinesq equation, is investigated. A generating function method starting from the Lax-Moser matrix is used to give an effective way to prove the involutivity of integrals. Finite-parameter solution of the Boussinesq equation is calculated based on the commutative system of ordinary differential equations with these integrals as Hamiltonians. The problem of the third order differential operator associated with the Boussinesq Neumann system put forward by H. Flaschka in 1983 is solved.展开更多
The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method f...The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.展开更多
文摘We present an eight component integrable Hamiltonian hierarchy, based on a reduced seventh order matrix spectral problem, with the aim of aiding the study and classification of multicomponent integrable models and their underlying mathematical structures. The zero-curvature formulation is the tool to construct a recursion operator from the spatial matrix problem. The second and third set of integrable equations present integrable nonlinear Schrödinger and modified Korteweg-de Vries type equations, respectively. The trace identity is used to construct Hamiltonian structures, and the first three Hamiltonian functionals so generated are computed.
基金supported by the Scientific Foundation of the Southeast University of China (Grant No.KJ2009359)the National Natural Science Foundation of China (Grant No.10871182)+1 种基金the U.S.Army Research Office (contract/grant number W911NF-08-1-0511)Texas grant NHARP 2010
文摘On the tangent bundle TSN-1 of the unit sphere SN-l, this paper reduces the coupled Burgers equations to two Neumann systems by using the nonlinearization of the Lax pair, whose Liouville integrability is displayed in the scheme of the r-matrix technique. Based on the Lax matrix of the Neumann systems, the Abel-Jacobi coordinates are appropriately chosen to straighten out the restricted Neumann flows on the complex torus, from which the new finite-gap solutions expressed by Riemann theta functions for the coupled Burgers equations are given in view of the Jacobi inversion.
基金Project supported by the National Natural Science Foundation of China (Grant Nos 90403019 and 10575080)
文摘This paper considers classical strings propagating in γ-deformed AdS3 γ S^3 backgrounds generated by certain shift T-dualities accompanied （TsT） transformations on S^3 and AdS3, respectively. It finds that the U（1） currents of strings with the twisted boundary conditions are equal to those in γ-deformed backgrounds generated by TsT transformations on both S3 and ADS3. Applying the TsT transformations, it derives the local Lax connections and the monodromy matrices in γ-deformed backgrounds with the spectral parameter which ensure the classical integrability of the string theories.
文摘Finite-dimensional integrable Hamiltonian system, obtained through the nonlinearization of the 3 × 3 spectral problem associated with the Boussinesq equation, is investigated. A generating function method starting from the Lax-Moser matrix is used to give an effective way to prove the involutivity of integrals. Finite-parameter solution of the Boussinesq equation is calculated based on the commutative system of ordinary differential equations with these integrals as Hamiltonians. The problem of the third order differential operator associated with the Boussinesq Neumann system put forward by H. Flaschka in 1983 is solved.
基金Supported by the National Basic Research Project forNonlinear Sciences and the Doctorate DissertationFoundation of Tsinghua University
文摘The r\|matrices and classical Poisson structures are constructed for x\| and t n\|constrained flows of the modified Jaulent\|Miodek (MJM) hierarchy.The Lax matrix is used to study the separation of variables method for these constrained flows. The Jacobi inversion problem for the MJM equation is obtained through the factorization of the MJM equation and the separability of the constrained flows. This is analogous to separation of variables for solving the MJM equation.
