Two binary Darboux transformations for the KdV hierarchy with self-consistent sources

Two binary (integral type) Darboux transformations for the KdV hierarchy with self-consistent sources are proposed. In contrast with the Darboux transformation for the KdV hierarchy, one of the two binary Darboux transformations provides non auto-B\"{a}cklund transformation between two n-th KdV equations with self-consistent sources with different degrees. The formula for the m-times repeated binary Darboux transformations are presented. This enables us to construct the N-soliton solution for the KdV hierarchy with self-consistent sources.Comment: 19 pages, LaTeX, no figures, to be published in Journal of Mathematical Physic

Separation of variables for soliton equations via their binary constrained flows

Binary constrained flows of soliton equations admitting $2\times 2$ Lax matrices have 2N degrees of freedom, which is twice as many as degrees of freedom in the case of mono-constrained flows. For their separation of variables only N pairs of canonical separated variables can be introduced via their Lax matrices by using the normal method. A new method to introduce the other N pairs of canonical separated variables and additional separated equations is proposed. The Jacobi inversion problems for binary constrained flows are established. Finally, the factorization of soliton equations by two commuting binary constrained flows and the separability of binary constrained flows enable us to construct the Jacobi inversion problems for some soliton hierarchies.Comment: 39 pages, Amste

Separable Hamiltonian equations on Riemann manifolds and related integrable hydrodynamic systems

A systematic construction of St\"{a}ckel systems in separated coordinates and its relation to bi-Hamiltonian formalism are considered. A general form of related hydrodynamic systems, integrable by the Hamilton-Jacobi method, is derived. One Casimir bi-Hamiltonian case is studed in details and in this case, a systematic construction of related hydrodynamic systems in arbitrary coordinates is presented, using a cofactor method and soliton symmetry constraints.Comment: to appear in Journal of Geometry and Physic

Character of frustration on magnetic correlation in doped Hubbard model

The magnetic correlation in the Hubbard model on a two-dimensional anisotropic triangular lattice is studied by using the determinant quantum Monte Carlo method. Around half filling, it is found that the increasing frustration $t'/t$ could change the wave vector of maximum spin correlation along ($\pi,\pi$)$\rightarrow$($\pi,\frac{5\pi}{6}$)$\rightarrow$($\frac{5\pi}{6},\frac{5\pi}{6}$)$\rightarrow$ ($\frac{2\pi}{3},\frac{2\pi}{3}$), indicating the frustration's remarkable effect on the magnetism. In the studied filling region =1.0-1.3, the doping behaves like some kinds of {\it{frustration}}, which destroys the $(\pi,\pi)$ AFM correlation quickly and push the magnetic order to a wide range of the $(\frac{2\pi}{3},\frac{2\pi}{3})$ $120^{\circ}$ order when the $t'/t$ is large enough. Our non-perturbative calculations reveal a rich magnetic phase diagram over both the frustration and electron doping.Comment: 6 pages, 7 figure

Driving Scene Perception Network: Real-time Joint Detection, Depth Estimation and Semantic Segmentation

As the demand for enabling high-level autonomous driving has increased in recent years and visual perception is one of the critical features to enable fully autonomous driving, in this paper, we introduce an efficient approach for simultaneous object detection, depth estimation and pixel-level semantic segmentation using a shared convolutional architecture. The proposed network model, which we named Driving Scene Perception Network (DSPNet), uses multi-level feature maps and multi-task learning to improve the accuracy and efficiency of object detection, depth estimation and image segmentation tasks from a single input image. Hence, the resulting network model uses less than 850 MiB of GPU memory and achieves 14.0 fps on NVIDIA GeForce GTX 1080 with a 1024x512 input image, and both precision and efficiency have been improved over combination of single tasks.Comment: 9 pages, 7 figures, WACV'1

A three-by-three matrix spectral problem for AKNS hierarchy and its binary Nonlinearization

A three-by-three matrix spectral problem for AKNS soliton hierarchy is proposed and the corresponding Bargmann symmetry constraint involved in Lax pairs and adjoint Lax pairs is discussed. The resulting nonlinearized Lax systems possess classical Hamiltonian structures, in which the nonlinearized spatial system is intimately related to stationary AKNS flows. These nonlinearized Lax systems also lead to a sort of involutive solutions to each AKNS soliton equation.Comment: 21pages, in Late