A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamilto...A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.展开更多
The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be ...The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.展开更多
In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for...In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.展开更多
We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, includi...We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, including the(2+1)-dimensional shallow water wave(SWW) hierarchy and the(2+1)-dimensional Kaup–Newell(KN)hierarchy. Through reduction of the(2+1)-dimensional hierarchies, we get a(2+1)-dimensional SWW equation and a(2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the(2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the(2+1)-dimensional KN equation could be deduced. Finally,with the help of the spatial spectral matrix of SWW hierarchy, we generate a(2+1) heat equation and a(2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang–Mills equations.展开更多
基金Supported by the Natural Science Foundation of China under Grant Nos. 61072147, 11071159, and 10971031by the Natural Science Foundation of Shanghai and Zhejiang Province under Grant Nos. 09ZR1410800 and Y6100791+1 种基金the Shanghai Shuguang Tracking Project under Grant No. 08GG01the Shanghai Leading Academic Discipline Project under Grant No. J50101
文摘A new isospectral problem is firstly presented, then we derive integrable system of soliton hierarchy. Also we obtain new integrable couplings of the generalized Kaup-Newell soliton equations hierarchy and its Hamiltonian structures by using Tu scheme and the quadratic-form identity. The method can be generalized to other soliton hierarchy.
基金Project supported by the National Natural Science Foundation of China (No.12071106) and the Science Foundation of the Ministry of Education of China.
文摘The authors give an algebraic method to add uniton numbers for harmonic maps from a simply connected domain ? ? R2∪{∞} into the unitary group U(N) with ?nite uniton number. So, it is proved that any n-uniton can be obtained from a 0-uniton by purely algebraic operations and integral transforms to solve the ?ˉ-problem via two different ways.
基金supported by Beijing Natural Science Foundation (Grant No. 1122008)the Scientific Research Common Program of Beijing Municipal Commission of Education (Grant No.KM201110005030)
文摘In this paper, we introduce the notion of generalized multiresolution structure (GMS) in the set-ting of reducing subspaces of L2(Rd). For a general expansive matrix, we obtain a necessary and sufficient condition for GMS, and prove the existence of GMS in a reducing subspace. Using GMS, we obtain a pyramid decomposition and a frame-like expansion for signals in reducing subspaces.
基金Supported by the National Natural Science Foundation of China under Grant No.11371361the Shandong Provincial Natural Science Foundation of China under Grant Nos.ZR2012AQ011,ZR2013AL016,ZR2015EM042+2 种基金National Social Science Foundation of China under Grant No.13BJY026the Development of Science and Technology Project under Grant No.2015NS1048A Project of Shandong Province Higher Educational Science and Technology Program under Grant No.J14LI58
文摘We introduce two operator commutators by using different-degree loop algebras of the Lie algebra A1,then under the framework of zero curvature equations we generate two(2+1)-dimensional integrable hierarchies, including the(2+1)-dimensional shallow water wave(SWW) hierarchy and the(2+1)-dimensional Kaup–Newell(KN)hierarchy. Through reduction of the(2+1)-dimensional hierarchies, we get a(2+1)-dimensional SWW equation and a(2+1)-dimensional KN equation. Furthermore, we obtain two Darboux transformations of the(2+1)-dimensional SWW equation. Similarly, the Darboux transformations of the(2+1)-dimensional KN equation could be deduced. Finally,with the help of the spatial spectral matrix of SWW hierarchy, we generate a(2+1) heat equation and a(2+1) nonlinear generalized SWW system containing inverse operators with respect to the variables x and y by using a reduction spectral problem from the self-dual Yang–Mills equations.
