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Perturbation to Mei symmetry and Mei adiabatic invariants for discrete generalized Birkhoffian system 被引量:3
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作者 张克军 方建会 李燕 《Chinese Physics B》 SCIE EI CAS CSCD 2011年第5期305-309,共5页
Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant i... Based on the concept of discrete adiabatic invariant, this paper studies the perturbation to Mei symmetry and Mei adiabatic invariants of the discrete generalized Birkhoffian system. The discrete Mei exact invariant induced from the Mei symmetry of the system without perturbation is given. The criterion of the perturbation to Mei symmetry is established and the discrete Mei adiabatic invariant induced from the perturbation to Mei symmetry is obtained. Meanwhile, an example is discussed to illustrate the application of the results. 展开更多
关键词 discrete generalized Birkhoffian system Mei symmetry PERTURBATION Mei adiabatic in-variant
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Symmetry and conserved quantities of discrete generalized Birkhoffian system 被引量:1
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作者 张克军 方建会 李燕 《Chinese Physics B》 SCIE EI CAS CSCD 2010年第12期356-361,共6页
The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete var... The Noether symmetry, the Mei symmetry and the conserved quantities of discrete generalized Birkhoffian system are studied in this paper. Using the difference discrete variational approach, the difference discrete variational principle of discrete generalized Birkhoffian system is derived. The discrete equations of motion of the system are established. The criterion of Noether symmetry and Mei symmetry of the system is given. The discrete Noether and Mei conserved quantities and the conditions for their existence are obtained. Finally, an example is given to show the applications of the results. 展开更多
关键词 discrete generalized Birkhoffian system Noether symmetry Mei symmetry conserved quantity
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Global Asymptotically Stable of a Generalized Discrete Ricker Competition System
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作者 Yoshihiro Hamaya 《Journal of Mathematics and System Science》 2013年第6期282-288,共7页
The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics... The purpose of this article is to investigate the sufficient conditions for the global asymptotic stability of one equilibrium point of a generalized Ricker competition system,……which appears as a model for dynamics with one extinct species, by applying the technique of average functions and the new principle of competitive exclusion. 展开更多
关键词 generalized discrete ricker competition systems average functions new principle of competitive exclusion.
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Dissipative Discrete System with Nearest-Neighbor Interaction for the Nonlinear Electrical Lattice
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作者 Saidou Abdoulkary Tibi Beda +3 位作者 Serge Y.Doka Fabien II Ndzana Louis Kavitha Alidou Mohamadou 《Journal of Modern Physics》 2012年第6期438-446,共9页
A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This ... A generalized dissipative discrete complex Ginzburg-Landau equation that governs the wave propagation in dissipative discrete nonlinear electrical transmission line with negative nonlinear resistance is derived. This equation presents arbitrarily nearest-neighbor nonlinearities. We analyze the properties of such model both in connection to their modulational stability, as well as in regard to the generation of intrinsic localized modes. We present a generalized discrete Lange-Newell criterion. Numerical simulations are performed and we show that discrete breathers are generated through modulational instability. 展开更多
关键词 generalized Dissipative discrete Complex Ginzburg-Landau Equation discrete Lange Newell-Criterion Pulse Trains Solitary Patterns
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Diverse soliton solutions and dynamical analysis of the discrete coupled mKdV equation with 4×4 Lax pair
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作者 刘雪珂 闻小永 《Chinese Physics B》 SCIE EI CAS CSCD 2023年第12期179-191,共13页
Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the co... Under consideration in this study is the discrete coupled modified Korteweg-de Vries(mKdV)equation with 4×4 Lax pair.Firstly,through using continuous limit technique,this discrete equation can be mapped to the coupled KdV and mKdV equations,which may depict the development of shallow water waves,the optical soliton propagation in cubic nonlinear media and the Alfven wave in a cold collision-free plasma.Secondly,the discrete generalized(r,N-r)-fold Darboux transformation is constructed and extended to solve this discrete coupled equation with the fourth-order linear spectral problem,from which diverse exact solutions including usual multi-soliton and semi-rational soliton solutions on the vanishing background,higher-order rational soliton and mixed hyperbolic-rational soliton solutions on the non-vanishing background are derived,and the limit states of some soliton and rational soliton solutions are analyzed by the asymptotic analysis technique.Finally,the numerical simulations are used to explore the dynamical behaviors of some exact soliton solutions.These results may be helpful for understanding some physical phenomena in fields of shallow water wave,optics,and plasma physics. 展开更多
关键词 discrete coupled mKdV equation continuous limit discrete generalized(r N-r)-fold Darboux transformation multi-soliton solutions rational soliton solutions
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Soliton interactions and asymptotic state analysis in a discrete nonlocal nonlinear self-dual network equation of reverse-space type
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作者 Cui-Lian Yuan Xiao-Yong Wen 《Chinese Physics B》 SCIE EI CAS CSCD 2021年第3期105-118,共14页
We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are const... We propose a reverse-space nonlocal nonlinear self-dual network equation under special symmetry reduction,which may have potential applications in electric circuits.Nonlocal infinitely many conservation laws are constructed based on its Lax pair.Nonlocal discrete generalized(m,N−m)-fold Darboux transformation is extended and applied to solve this system.As an application of the method,we obtain multi-soliton solutions in zero seed background via the nonlocal discrete N-fold Darboux transformation and rational solutions from nonzero-seed background via the nonlocal discrete generalized(1,N−1)-fold Darboux transformation,respectively.By using the asymptotic and graphic analysis,structures of one-,two-,three-and four-soliton solutions are shown and discussed graphically.We find that single component field in this nonlocal system displays unstable soliton structure whereas the combined potential terms exhibit stable soliton structures.It is shown that the soliton structures are quite different between discrete local and nonlocal systems.Results given in this paper may be helpful for understanding the electrical signals propagation. 展开更多
关键词 reverse-space nonlocal nonlinear self-dual network equation nonlocal discrete generalized(m N−m)-fold Darboux transformation multi-soliton solutions rational solutions
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THE MULTIPLICATIVE COMPLEXITY AND ALGORITHM OF THE GENERALIZED DISCRETE FOURIER TRANSFORM(GFT)
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作者 Y.H. Zeng(7th Department, National University of Defence Technology, Changsha, China) 《Journal of Computational Mathematics》 SCIE CSCD 1995年第4期351-356,共6页
In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a l... In this paper, we have proved that the lower bound of the number of real multiplications for computing a length 2(t) real GFT(a,b) (a = +/-1/2, b = 0 or b = +/-1/2, a = 0) is 2(t+1) - 2t - 2 and that for computing a length 2t real GFT(a,b)(a = +/-1/2, b = +/-1/2) is 2(t+1) - 2. Practical algorithms which meet the lower bounds of multiplications are given. 展开更多
关键词 DCT II THE MULTIPLICATIVE COMPLEXITY AND ALGORITHM OF THE generalized discrete FOURIER TRANSFORM Math GFT
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Interactions of Soliton Waves for a Generalized Discrete KdV Equation
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作者 Tong Zhou Zuo-Nong Zhu 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第7期6-12,共7页
It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons i... It is well known that soliton interactions in discrete integrable systems often possess new properties which are different from the continuous integrable systems, e.g., we found that there are such discrete solitons in a semidiserete integrable system (the time variable is continuous and the space one is discrete) that the shorter solitary waves travel faster than the taller ones. Very recently, this kind of soliton was also observed in a full discrete generalized KdV system (the both of time and space variables are discrete) introduced by Kanki et al. In this paper, for the generalized discrete KdV (gdKdV) equation, we describe its richer structures of one-soliton solutions. The interactions of two-soliton waves to the gdKdV equation are studied. Some new features of the soliton interactions are proposed by rigorous theoretical analysis. 展开更多
关键词 generalized discrete KdV equation soliton solution soliton interaction
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Discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type 被引量:5
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作者 杨恩浩 《Acta Mathematica Sinica,English Series》 SCIE CSCD 1990年第3期230-242,共13页
We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.A... We establish some new n-independent-variable discrete inequalities which are analo- gous to some Langenhop-Gollwitzer type integral inequalities obtained by the present author in J. Math.Anal.Appl.,109(1985),171-181.An application to hyperbolic summary-difference equations in n variables is also sketched. 展开更多
关键词 discrete Generalizations of Some N-Independent-Variable Integral Inequalities of Langenhop-Gollwitzer Type
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Integrability, multi-soliton and rational solutions, and dynamical analysis for a relativistic Toda lattice system with one perturbation parameter 被引量:1
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作者 Meng-Li Qin Xiao-Yong Wen Cui-Lian Yuan 《Communications in Theoretical Physics》 SCIE CAS CSCD 2021年第6期13-42,共30页
Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameterαabbreviated as RTLαsystem by Suris,which may describe the motions of particles in lattices interacting through ... Under investigation in this paper is a relativistic Toda lattice system with one perturbation parameterαabbreviated as RTLαsystem by Suris,which may describe the motions of particles in lattices interacting through an exponential interaction force.First of all,an integrable lattice hierarchy associated with an RTLαsystem is constructed,from which some relevant integrable properties such as Hamiltonian structures,Liouville integrability and conservation laws are investigated.Secondly,the discrete generalized(m,2 N-m)-fold Darboux transformation is constructed to derive multi-soliton solutions,higher-order rational and semirational solutions,and their mixed solutions of an RTLαsystem.The soliton elastic interactions and details of rational solutions are analyzed via the graphics and asymptotic analysis.Finally,soliton dynamical evolutions are investigated via numerical simulations,showing that a small noise has very little effect on the soliton propagation.These results may provide new insight into nonlinear lattice dynamics described by RTLαsystem. 展开更多
关键词 RTLαsystem Hamiltonian structures discrete generalized(m 2N-m)-fold Darboux transformation soliton and rational solutions asymptotic analysis
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Construction of Optimal Mixed-Level Uniform Designs
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作者 CHATTERJEE Kashinath LIU Min-Qian +1 位作者 QIN Hong YANG Liuqing 《Journal of Systems Science & Complexity》 SCIE EI CSCD 2024年第2期841-862,共22页
The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments.The generalized discrete discrepancy is proposed to evaluate the uniformity of the mix... The theory of uniform design has received increasing interest because of its wide application in the field of computer experiments.The generalized discrete discrepancy is proposed to evaluate the uniformity of the mixed-level factorial design.In this paper,the authors give a lower bound of the generalized discrete discrepancy and provide some construction methods of optimal mixed-level uniform designs which can achieve this lower bound.These methods are all deterministic construction methods which can avoid the complexity of stochastic algorithms.Both saturated mixed-level uniform designs and supersaturated mixed-level uniform designs can be obtained with these methods.Moreover,the resulting designs are also χ^(2)-optimal and minimum moment aberration designs. 展开更多
关键词 generalized discrete discrepancy Hadamard matrix mixed-level design orthogonal array supersaturated design
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