The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as ...The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.展开更多
In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） wi...In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.展开更多
为了进一步提高分布式阵列的自由度和分辨力,提出一种分布式nested阵列。该阵列将nested阵列作为分布式阵列的子阵。基于Khatri-Rao积,nested子阵可提高整个阵列的自由度。分布式nested阵列以较少的阵元数及硬件成本实现大的孔径和较高...为了进一步提高分布式阵列的自由度和分辨力,提出一种分布式nested阵列。该阵列将nested阵列作为分布式阵列的子阵。基于Khatri-Rao积,nested子阵可提高整个阵列的自由度。分布式nested阵列以较少的阵元数及硬件成本实现大的孔径和较高的分辨力,而且提高了目标波达方向(direction of arrival,DOA)估计的精度。并利用基于Khatri-Rao积的空间平滑酉旋转不变子空间(estimation of signal parameters via rotational invariance techniques,ESPRIT)算法进行DOA估计。其先对协方差矩阵向量化提高自由度,然后利用空间平滑对新数据协方差矩阵进行秩恢复,最后使用双尺度酉ESPRIT算法得到DOA估计。仿真结果证明所提方法的有效性。展开更多
The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonl...The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.展开更多
为了提高分布式阵列在低信噪比(signal-to-noise ratio,SNR)条件下的波达方向(direction-of-arrival,DOA)估计性能,同时放宽阵列物理孔径扩展程度的限制,提出了一种基于旋转不变子空间(estimation of signal parameters via rotational ...为了提高分布式阵列在低信噪比(signal-to-noise ratio,SNR)条件下的波达方向(direction-of-arrival,DOA)估计性能,同时放宽阵列物理孔径扩展程度的限制,提出了一种基于旋转不变子空间(estimation of signal parameters via rotational invariance techniques,ESPRIT)的多基线分布式阵列DOA估计方法。该方法通过优化分布式阵列结构,在子阵间使用多基线结构布阵,结合ESPRIT算法和多步解模糊方法得到多基线分布式阵列的高精度无模糊DOA估计。此外,利用最大后验概率准则近似法分析分布式阵列DOA估计的门限效应,给出了SNR门限和基线长度门限的近似计算方法。计算机仿真结果验证了所提方法的有效性。展开更多
基金supported by the State Administration of Foreign Experts Affairs of China,National Natural Science Foundation of China (Grant Nos. 10971136,10831003,61072147,11071159)Chunhui Plan of the Ministry of Education of China,Zhejiang Innovation Project (Grant No. T200905)the Natural Science Foundation of Shanghai and the Shanghai Leading Academic Discipline Project (Grant No.J50101)
文摘The invariant subspace method is refined to present more unity and more diversity of exact solutions to evolution equations. The key idea is to take subspaces of solutions to linear ordinary differential equations as invariant subspaces that evolution equations admit. A two-component nonlinear system of dissipative equations is analyzed to shed light oi1 the resulting theory, and two concrete examples are given to find invariant subspaces associated with 2nd-order and 3rd-order linear ordinary differentii equations and their corresponding exact solutions with generalized separated variables.
基金Project supported by the National Natural Science Foundation of China for Distinguished Young Scholars (No.10925104)the National Natural Science Foundation of China (No.11001240)+1 种基金the Doctoral Program Foundation of the Ministry of Education of China (No.20106101110008)the Zhejiang Provincial Natural Science Foundation of China (Nos.Y6090359,Y6090383)
文摘In this paper, the dimension of invariant subspaces admitted by nonlinear sys- tems is estimated under certain conditions. It is shown that if the two-component nonlinear vector differential operator F = （F1, F2） with orders {k1, k2} （k1≥ k2） preserves the invariant subspace Wn1^1× Wn2^2 （n1 ≥ n2）, then n1 - n2 ≤ k2, n1 ≤2（k1 ＋ k2） ＋ 1, where Wnq^q is the space generated by solutions of a linear ordinary differential equation of order nq （q = 1, 2）. Several examples including the （1＋1）-dimensional diffusion system and Ito＇s type, Drinfel＇d-Sokolov-Wilson＇s type and Whitham-Broer-Kaup＇s type equations are presented to illustrate the result. Furthermore, the estimate of dimension for m-component nonlinear systems is also given.
文摘为了进一步提高分布式阵列的自由度和分辨力,提出一种分布式nested阵列。该阵列将nested阵列作为分布式阵列的子阵。基于Khatri-Rao积,nested子阵可提高整个阵列的自由度。分布式nested阵列以较少的阵元数及硬件成本实现大的孔径和较高的分辨力,而且提高了目标波达方向(direction of arrival,DOA)估计的精度。并利用基于Khatri-Rao积的空间平滑酉旋转不变子空间(estimation of signal parameters via rotational invariance techniques,ESPRIT)算法进行DOA估计。其先对协方差矩阵向量化提高自由度,然后利用空间平滑对新数据协方差矩阵进行秩恢复,最后使用双尺度酉ESPRIT算法得到DOA估计。仿真结果证明所提方法的有效性。
基金supported by National Natural Science Foundation of China for Distinguished Young Scholars(Grant No.10925104)the PhD Programs Foundation of Ministry of Education of China(Grant No.20106101110008)the United Funds of NSFC and Henan for Talent Training(Grant No.U1204104)
文摘The inhomogeneous nonlinear diffusion equation is studied by invariant subspace and condi- tional Lie=Bgcklund symmetry methods. It is shown that the equations admit a class of invariant subspaces governed by the nonlinear ordinary differential equations, which is equivalent to a kind of higher=order conditional Lie-B^icklund symmetries of the equations. As a consequence, a number of new solutions to the inhomogeneous nonlinear diffusion equations are constructed explicitly or reduced to solving finite-dimensional dynamical sys- tems.
文摘为了提高分布式阵列在低信噪比(signal-to-noise ratio,SNR)条件下的波达方向(direction-of-arrival,DOA)估计性能,同时放宽阵列物理孔径扩展程度的限制,提出了一种基于旋转不变子空间(estimation of signal parameters via rotational invariance techniques,ESPRIT)的多基线分布式阵列DOA估计方法。该方法通过优化分布式阵列结构,在子阵间使用多基线结构布阵,结合ESPRIT算法和多步解模糊方法得到多基线分布式阵列的高精度无模糊DOA估计。此外,利用最大后验概率准则近似法分析分布式阵列DOA估计的门限效应,给出了SNR门限和基线长度门限的近似计算方法。计算机仿真结果验证了所提方法的有效性。
