Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transforma...Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.展开更多
证明了三维空间中一类耦合非线性Schr d inger方程组的Cauchy问题iut+△u=a|u|α-1u|v|β+1,ivt+△v=b|u|α+1|v|β-1v,u(0,x)=u0(x),v(0,x)=v0(x),t>0,x∈Rn,整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有的较强的衰...证明了三维空间中一类耦合非线性Schr d inger方程组的Cauchy问题iut+△u=a|u|α-1u|v|β+1,ivt+△v=b|u|α+1|v|β-1v,u(0,x)=u0(x),v(0,x)=v0(x),t>0,x∈Rn,整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有的较强的衰减估计.展开更多
The field experiment is conducted from April 16, 2005 to July 20, 2005 at Wenchang area east of Hainan Island （19~35＇N, l12~E） of China. Internal wave packets are observed frequently with thermistor chains during t...The field experiment is conducted from April 16, 2005 to July 20, 2005 at Wenchang area east of Hainan Island （19~35＇N, l12~E） of China. Internal wave packets are observed frequently with thermistor chains during the experiment. Meanwhile, internal waves are also detected from a synthetic aperture radar （SAR） image on June 19, 2005 and several other moderate-resolution imaging spectroradiometer （MODIS） images near a mooring position. The distance between the positive and negative peaks induced by the internal wave can be obtained from satellite images. Combined with remote sensing images and in situ data, a new method to inverse the amplitude of the internal wave is proposed based on a corrected nonlinear Schr6dinger （NLS） equation. Two relationships are given between the peak-to-peak distance and the characteristic wavelength of the internal wave for different nonlinear and dispersion coefficients. Based on the satellite images, the amplitude inversion of the internal waves are carried out with the NLS equation as well as the KdV equation. The calculated amplitudes of the NLS equation are close to the observation amplitude which promise the NLS equation a reliable method.展开更多
Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. L...Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/2△Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some LP（Hn）, where b ∈ BMO（Hn）. Note that the kernel of Ti, i = 1, 2, 3 has no smoothness.展开更多
A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a G...A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.展开更多
Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We fur...Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.展开更多
基金Project supported by the National Natural Science Foundation of China （Grant No. 10772110） and the Natural Science Foundation of Zhejiang Province, China （Grant Nos. Y606049, Y6090681, and Y6100257）.
文摘Analytical solutions in terms of rational-like functions are presented for a （3＋1）-dimensional nonlinear Schrodinger equation with time-varying coefficients and a harmonica potential using the similarity transformation and a direct ansatz. Several free functions of time t are involved to generate abundant wave structures. Three types of elementary functions are chosen to exhibit the corresponding nonlinear rogue wave propagations.
文摘证明了三维空间中一类耦合非线性Schr d inger方程组的Cauchy问题iut+△u=a|u|α-1u|v|β+1,ivt+△v=b|u|α+1|v|β-1v,u(0,x)=u0(x),v(0,x)=v0(x),t>0,x∈Rn,整体解的存在唯一性,并得到了解关于初值的连续依赖性及解具有的较强的衰减估计.
基金The National Natural Science Foundation of China under contract Nos 61171161 and 61471136the National High Technology Research and Development Program(863 Program)of China under contract No.2013AA09A502
文摘The field experiment is conducted from April 16, 2005 to July 20, 2005 at Wenchang area east of Hainan Island （19~35＇N, l12~E） of China. Internal wave packets are observed frequently with thermistor chains during the experiment. Meanwhile, internal waves are also detected from a synthetic aperture radar （SAR） image on June 19, 2005 and several other moderate-resolution imaging spectroradiometer （MODIS） images near a mooring position. The distance between the positive and negative peaks induced by the internal wave can be obtained from satellite images. Combined with remote sensing images and in situ data, a new method to inverse the amplitude of the internal wave is proposed based on a corrected nonlinear Schr6dinger （NLS） equation. Two relationships are given between the peak-to-peak distance and the characteristic wavelength of the internal wave for different nonlinear and dispersion coefficients. Based on the satellite images, the amplitude inversion of the internal waves are carried out with the NLS equation as well as the KdV equation. The calculated amplitudes of the NLS equation are close to the observation amplitude which promise the NLS equation a reliable method.
基金Supported by the National Natural Science Foundation under Grant(11147180)Science and Technology Agency Foundation of Hubei Province under Grant(2011CDC005,D20122804)
基金supported by NSFC 11171203, S2011040004131STU Scientific Research Foundation for Talents TNF 10026+1 种基金supported by NSFC No.10990012,10926179RFDP of China No.200800010009
文摘Let L = -△Hn ＋ V be a SchrSdinger operator on Heisenberg group Hn, where AHn is the sublaplacian and the nonnegative potential V belongs to the reverse HSlder class BQ/2 where Q is the homogeneous dimension of Hn. Let T1 = （--△Hn ＋V）-1V, T2 = （-△Hn ＋V）-1/2V1/2, and T3 = （--AHn ＋V）-I/2△Hn, then we verify that [b, Ti], i = 1, 2, 3 are bounded on some LP（Hn）, where b ∈ BMO（Hn）. Note that the kernel of Ti, i = 1, 2, 3 has no smoothness.
基金supported by the National Natural Science Foundation of China(Nos.11502103 and11421062)the Open Fund of State Key Laboratory of Structural Analysis for Industrial Equipment of China(No.GZ15115)
文摘A sampling approximation for a function defined on a bounded interval is proposed by combining the Coiflet-type wavelet expansion and the boundary extension technique. Based on such a wavelet approximation scheme, a Galerkin procedure is developed for the spatial discretization of the generalized nonlinear Schr6dinger （NLS） equa- tions, and a system of ordinary differential equations for the time dependent unknowns is obtained. Then, the classical fourth-order explicit Runge-Kutta method is used to solve this semi-discretization system. To justify the present method, several widely considered problems are solved as the test examples, and the results demonstrate that the proposed wavelet algorithm has much better accuracy and a faster convergence rate in space than many existing numerical methods.
文摘Let H be a Schroedinger operator on R^n. Under a polynomial decay condition for the kernel of its spectral operator, we show that the Besov spaces and Triebel-Lizorkin spaces associated with H are well defined. We further give a Littlewood-Paley characterization of Lp spaces in terms of dyadic functions of H. This generalizes and strengthens the previous result when the heat kernel of H satisfies certain upper Gaussian bound.
