检索结果-南通市图书馆

Cauchy matrix approach to three non-isospectral nonlinear Schrödinger equations

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第5期76卷 1-15页

作者： Alemu Yilma Tefera Shangshuai Li da-jun zhang Department of Mathematics Shanghai UniversityShanghai 200444China Newtouch Center for Mathematics of Shanghai University Shanghai 200444China Department of Applied Mathematics Faculty of Science and EngineeringWaseda UniversityTokyo 169-8555Japan

This paper aims to develop a direct approach,namely,the Cauchy matrix approach,to non-isospectral integrable *** the Cauchy matrix approach,the Sylvester equation plays a central role,which defines a dressed Cauchy matrix to provideτfunctions for the investigated *** this paper,using the Cauchy matrix approach,we derive three non-isospectral nonlinear Schrödinger equations and their explicit *** equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral *** solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schrödinger equations through complex *** solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

关键词： Cauchy matrix approach Sylvester equation nonlinear Schrödinger equation non-isospectral integrable system explicit solution

Cauchy matrix approach to three non-isospectral nonlinear Schr?dinger equations

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2024年第5期 3-17页

作者： Alemu Yilma Tefera Shangshuai Li da-jun zhang Department of Mathematics Shanghai University Newtouch Center for Mathematics of Shanghai University Department of Applied Mathematics Faculty of Science and Engineering Waseda University

This paper aims to develop a direct approach, namely, the Cauchy matrix approach, to non-isospectral integrable systems. In the Cauchy matrix approach, the Sylvester equation plays a central role, which defines a dressed Cauchy matrix to provide τ functions for the investigated equations. In this paper, using the Cauchy matrix approach, we derive three non-isospectral nonlinear Schr?dinger equations and their explicit solutions. These equations are generically related to the time-dependent spectral parameter in the Zakharov–Shabat–Ablowitz–Kaup–Newell–Segur spectral problem. Their solutions are obtained from the solutions of unreduced non-isospectral nonlinear Schr?dinger equations through complex reduction. These solutions are analyzed and illustrated to show the non-isospectral effects in dynamics of solitons.

关键词：

Vector NLS solitons interacting with a boundary

在线全文

同方期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2021年第4期73卷 45-51页

作者： Cheng zhang da-jun zhang Department of Mathematics Shanghai UniversityShanghai200444China

We construct multi-soliton solutions of the n-component vector nonlinear Schrödinger equation on the half-line subject to two classes of integrable boundary conditions(BCs):the homogeneous Robin BCs and the mixed Neumann/Dirichlet *** construction is based on the so-called dressing the boundary,which generates soliton solutions by preserving the integrable BCs at each step of the darboux-dressing *** the Robin BCs,examples,including boundary-bound solitons,are explicitly derived;under the mixed Neumann/Dirichlet BCs,the boundary can act as a polarizer that tunes different components of the vector *** of our construction to the inverse scattering transform is also provided.

关键词： polarizer effect solitons on the half-line vector nonlinear Schrödinger equation integrable boundary conditions boundary-bound states

Addition formulae, Backlund transformations, periodic solutions, and quadrilateral equations

在线全文

学校读者我要写书评

暂无评论

Frontiers of Mathematics in China 2019年第1期14卷 203-223页

作者： danda zhang da-jun zhang School of Mathematics and Statistics Ningbo University Ningbo 315211 China Department of Mathematics Shanghai University Shanghai 200444 China

Addition formulae of trigonometric and elliptic functions are used to generate Backlund transformations together with their connecting quadrilateral equations. As a result, we obtain the periodic solutions for a numbe... 详细信息

关键词： Addition formulae trigonometric functions elliptic functions Backlund transformation quadrilateral equations

Conserved Gross-Pitaevskii equations with a parabolic potential

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2022年第10期74卷 30-36页

作者： Shi-min Liu da-jun zhang Department of Mathematics Shanghai UniversityShanghai 200444People’s Republic of China

An integrable Gross–Pitaevskii equation with a parabolic potential is presented where particle density|u|^(2)is *** also present an integrable vector Gross–Pitaevskii system with a parabolic potential,where the total particle density∑^(n)_(j)=_(1)∣u_(j)∣^(2)is *** equations are related to nonisospectral scalar and vector nonlinear Schrödinger *** many conservation laws are *** transformations between the standard isospectral nonlinear Schrödinger equations and the conserved Gross–Pitaevskii equations,both scalar and vector cases are *** and dynamics are analyzed and *** solutions exhibit features of localized-like waves.

关键词： Gross-Pitaevskii equation gauge transformation nonisospectral conserved particle density

Cauchy matrix structure of the Mel’nikov model of long-short wave interaction

在线全文

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2020年第12期72卷 83-93页

作者： Hong-Juan Tian da-jun zhang Department of Mathematics Shanghai UniversityShanghai 200444China

We propose a systematic method to construct the Mel’nikov model of long–short wave interactions,which is a special case of the Kadomtsev–Petviashvili(KP)equation with self-consistent sources(KPSCS).We show details how the Cauchy matrix approach applies to Mel’nikov’s model which is derived as a complex reduction of the *** a new result wefind that in the dispersion relation of a 1-soliton there is an arbitrary time-dependent function that has previously not reported in the literature about the Mel’nikov *** function brings time variant velocity for the long wave and also governs the short-wave *** variety of interactions of waves resulting from the time-freedom in the dispersion relation is illustrated.

关键词： Mel’nikov model of long–short wave interaction Cauchy matrix approach self-consistent sources KP equation

Physics of cavitation near particles

在线全文

学校读者我要写书评

暂无评论

Journal of Hydrodynamics 2024年第1期36卷 102-118页

作者： Jia-xin Yu Xiao-yu Wang jun-wei Shen Jin-sen Hu Xiang-qing zhang da-qing He Yu-ning zhang Key Laboratory of Power Station Energy Transfer Conversion and System(Ministry of Education) School of Energy Power and Mechanical EngineeringNorth China Electric Power UniversityBeijing102206China

The combined effect of cavitation and silt abrasion presents a great challenge and threat to secure the operation and the efficiency of hydraulic machineries working in sediment-laden *** present paper critically reviews the current research progress on the interaction mechanisms of the bubbles and the ***,the analytical models including boundary treatment methods for predicting the jet dynamics of the bubble collapse near particles are ***,the bubble collapsing dynamics,jet dynamics and shock wave characteristics near particles are revealed both experimentally and ***,the bubble-particle-wall system is investigated with a focus on microjets.

关键词： Cavitation bubble particle jet shock wave

Nonisospectral effects on generating localized waves

在线全文

维普期刊数据库

学校读者我要写书评

暂无评论

Communications in Theoretical Physics 2021年第11期73卷 18-30页

作者： Abdselam Silem Hua Wu da-jun zhang Department of Mathematics Shanghai UniversityShanghai 200444China

In this paper we explain how space-time localized waves can be generated by introducing nonisospectral effects which are usually related to non-uniformity of *** nonisospectral Korteweg–de Vries,modified Korteweg–de Vries and the Hirota equations are employed to demonstrate the *** solutions are presented in terms of Wronskians and double Wronskians and space-time localized dynamics are illustrated.

关键词： nonisospectral effects space-time localized wave integrable system bilinear

Geometric Error Identification of Gantry-Type CNC Machine Tool Based on Multi-Station Synchronization Laser Tracers

在线全文

学校读者我要写书评

暂无评论

Chinese Journal of Mechanical Engineering 2024年第2期37卷 150-162页

作者： jun Zha Huijie zhang School of Mechanical Engineering Xi’an Jiaotong UniversityXi’an 710049China Xi’an Jiaotong University Suzhou Academy Suzhou 215123China

Laser tracers are a three-dimensional coordinate measurement system that are widely used in industrial *** propose a geometric error identification method based on multi-station synchronization laser tracers to enable the rapid and high-precision measurement of geometric errors for gantry-type computer numerical control(CNC)machine *** method also improves on the existing measurement efficiency issues in the single-base station measurement method and multi-base station time-sharing measurement *** consider a three-axis gantry-type CNC machine tool,and the geometric error mathematical model is derived and established based on the combination of screw theory and a topological analysis of the machine kinematic *** four-station laser tracers position and measurement points are realized based on the multi-point positioning principle.A self-calibration algorithm is proposed for the coordinate calibration process of a laser tracer using the Levenberg-Marquardt nonlinear least squares method,and the geometric error is solved using Taylor’s first-order linearization *** experimental results show that the geometric error calculated based on this modeling method is comparable to the results from the Etalon laser *** a volume of 800 mm×1000 mm×350 mm,the maximum differences of the linear,angular,and spatial position errors were 2.0μm,2.7μrad,and 12.0μm,respectively,which verifies the accuracy of the proposed *** research proposes a modeling method for the precise measurement of errors in machine tools,and the applied nature of this study also makes it relevant both to researchers and those in the industrial sector.

关键词： Multi-point positioning Multi-station synchronization CNC machine tool Geometric error Error separation