共查询到20条相似文献,搜索用时 15 毫秒
1.
In this paper, we investigate a modified differential-difference KP equation which is shown to have a continuum limit into the mKP equation. It is also shown that the solution of the modified differential-difference KP equation is related to the solution of the differential-difference KP equation through a Miura transformation. We first present the Grammian solution to the modified differential-difference KP equation, and then produce a coupled modified differential-difference KP system by applying the source generation procedure. The explicit N-soliton solution of the resulting coupled modified differential-difference system is expressed in compact forms by using the Grammian determinant and Casorati determinant. We also construct and solve another form of the self-consistent sources extension of the modified differential-difference KP equation, which constitutes a Bäcklund transformation for the differential-difference KP equation with self-consistent sources. 相似文献
2.
In this paper, an extended Riccati sub-ODE method is proposed to establish new exact solutions for fractional differential-difference equations in the sense of modified Riemann-Liouville derivative. By a fractional complex transformation, a given fractional differential-difference equation can be turned into another differential-difference equation of integer order. The validity of the method is illustrated by applying it to solve the fractional Hybrid lattice equation and the fractional relativistic Toda lattice system. As a result, some new exact solutions including hyperbolic function solutions, trigonometric function solutions and rational solutions are established. 相似文献
3.
smail Aslan 《理论物理通讯》2014,(5):595-599
The extended simplest equation method is used to solve exactly a new differential-difference equation of fractional-type, proposed by Narita [J. Math. Anal. Appl. 381 (2011) 963] quite recently, related to the discrete MKdV equation. It is shown that the model supports three types of exact solutions with arbitrary parameters: hyperbolic, trigonometric and rational, which have not been reported before. 相似文献
4.
Wildon Fickett 《Physica D: Nonlinear Phenomena》1985,16(3):358-370
Using a set of model equations for reactive flow, we study the stability of a “square-wave” detonation, in which each particle of the fluid reacts instantaneously after an induction time which depends on how hard it was shocked. We obtain a differential-difference equation for the shock velocity, valid for small perturbations about the steady solution. This equation is of so-called “advanced” type, in which the velocity at a given time depends on both velocity and acceleration at an earlier time. 相似文献
5.
This paper proposes two lattice traffic models by taking into
account the drivers' delay in response. The lattice versions of the
hydrodynamic model are described by the differential-difference
equation and difference-difference equation, respectively. The
stability conditions for the two models are obtained by using the
linear stability theory. The modified KdV equation near the critical
point is derived to describe the traffic jam by using the reductive
perturbation method, and the kink--antikink soliton solutions related
to the traffic density waves are obtained. The results show that the
drivers' delay in sensing headway plays an important role in jamming
transition. 相似文献
6.
The modified discrete KP equation is the Bäcklund transformation for the Hirota’s discrete KP equation or the Hirota-Miwa equation. We construct the modified discrete KP equation with self-consistent sources via source generation procedure and clarify the algebraic structure of the resulting coupled modified discrete KP system by presenting its discrete Gram-type determinant solutions. It is also shown that the commutativity between the source generation procedure and Bäcklund transformation is valid for the discrete KP equation. Finally, we demonstrate that the modified discrete KP equation with self-consistent sources yields the modified differential-difference KP equation with self-consistent sources through a continuum limit. The continuum limit of an explicit solution to the modified discrete KP equation with self-consistent sources also gives the explicit solution for the modified differential-difference KP equation with self-consistent sources. 相似文献
7.
In this Letter, we generalize the differential transform method to solve differential-difference equation for the first time. Two simple but typical examples are applied to illustrate the validity and the great potential of the generalized differential transform method in solving differential-difference equation. A Padé technique is also introduced and combined with GDTM in aim of extending the convergence area of presented series solutions. Comparisons are made between the results of the proposed method and exact solutions. Then we apply the differential transform method to the discrete KdV equation and the discrete mKdV equation, and successfully obtain solitary wave solutions. The results reveal that the proposed method is very effective and simple. We should point out that generalized differential transform method is also easy to be applied to other nonlinear differential-difference equation. 相似文献
8.
Alexander V. Mikhailov Georgios Papamikos Jing Ping Wang 《Letters in Mathematical Physics》2016,106(7):973-996
We propose a method for construction of Darboux transformations, which is a new development of the dressing method for Lax operators invariant under a reduction group. We apply the method to the vector sine-Gordon equation and derive its Bäcklund transformations. We show that there is a new Lax operator canonically associated with our Darboux transformation resulting an evolutionary differential-difference system on a sphere. The latter is a generalised symmetry for the chain of Bäcklund transformations. Using the re-factorisation approach and the Bianchi permutability of the Darboux transformations, we derive new vector Yang–Baxter map and integrable discrete vector sine-Gordon equation on a sphere. 相似文献
9.
A new lattice model of traffic flow with the consideration of the driver?s forecast effects 总被引:2,自引:0,他引:2
In this Letter, a new lattice model is presented with the consideration of the driver?s forecast effects (DFE). The linear stability condition of the extended model is obtained by using the linear stability theory. The analytical results show that the new model can improve the stability of traffic flow by considering DFE. The modified KdV equation near the critical point is derived to describe the traffic jam by nonlinear analysis. Numerical simulation also shows that the new model can improve the stability of traffic flow by adjusting the driver?s forecast intensity parameter, which is consistent with the theoretical analysis. 相似文献
10.
《Physics letters. A》1999,259(2):135-139
Exact solutions of the first order differential equation with delay are derived. The equation has been introduced as a model of traffic flow. The solution describes the traveling cluster of jam, which is characterized by Jacobi's elliptic function. The induced differential-difference equations are related to some soliton systems. 相似文献
11.
《Physics letters. A》1999,259(1):71-79
The propagation of a localized excitation and the thermodynamic properties in DNA double helices due to stretching vibration of hydrogen bond are discussed. The stretch of the hydrogen bonds is considered as a nonlinear chain with cubic and quartic potential. The analytic solution of the solitary wave is obtained by using the continuum approximation and its stability has been discussed. With the help of the thermodynamic Green function technique, the temperature and anharmonicity effects on the thermodynamic properties of DNA are investigated. The theoretical calculation of the specific heat in DNA at low temperature is consistent with the experimental result. The numerical simulation of the differential-difference equation shows that the solitary wave is pinned by the lattice. It is also pointed out that the conformatioal transitions from B-DNA to A-DNA can occur in the case of asymmetry potential with quartic term. 相似文献
12.
One of the oldest unresolved problems in fluid mechanics is the nature of liquid flow along solid surfaces. It is traditionally assumed that across the liquid-solid interface, liquid and solid speeds exactly match. However, recent observations document that on the molecular scale, liquids can slip relative to solids. We formulate a model in which the liquid dynamics are described by a stochastic differential-difference equation, related to the Frenkel-Kontorova equation. The model, in agreement with molecular dynamics simulations, reveals that slip occurs via two mechanisms: localized defect propagation and concurrent slip of large domains. Well-defined transitions occur between the two mechanisms. 相似文献
13.
Christine C. Dantas 《Foundations of Physics》2013,43(2):236-242
The quantum evolution equation of Loop Quantum Cosmology (LQC)—the quantum Hamiltonian constraint—is a difference equation. We relate the LQC constraint equation in vacuum Bianchi I separable (locally rotationally symmetric) models with an integrable differential-difference nonlinear Schrödinger type equation, which in turn is known to be associated with integrable, discrete Heisenberg spin chain models in condensed matter physics. We illustrate the similarity between both systems with a simple constraint in the linear regime. 相似文献
14.
In this paper, we obtain a 1 1 dimensional integrable differential-difference model for the sine-Gordon equation by Hirota's discretization method. A bilinear B(a)cklund transformation and the associated Lax pair are also proposed for this model. 相似文献
15.
Considering the effect of multiple flux difference, an extended lattice model is proposed to improve the stability of traffic flow. The stability condition of the new model is obtained by using linear stability theory. The theoretical analysis result shows that considering the flux difference effect ahead can stabilize traffic flow. The nonlinear analysis is also conducted by using a reductive perturbation method. The modified KdV (mKdV) equation near the critical point is derived and the kink-antikink solution is obtained from the mKdV equation. Numerical simulation results show that the multiple flux difference effect can suppress the traffic jam considerably, which is in line with the analytical result. 相似文献
16.
A new method for constructing the Wronskian entries is proposed and
applied to the differential-difference
Kadomtsev-Petviashvilli (DΔKP) equation. The generalized
Wronskian solutions to it are obtained, including rational solutions
and Matveev solutions. 相似文献
17.
Amal K. Das 《Physica A》1982,110(3):489-500
A model previously discussed by the author to study Brownian motion of charged carriers in a quantizing magnetic field is extended to include a Landau level-dependent friction parameter. A phase-space Fokker-Planck equation is used to derive a generalized diffusion equation describing spatial diffusion of the carriers, coupled with random jumps between adjacent Landau levels. This partial differential-difference equation is solved analytically. The longitudinal “global” diffusion coefficient is calculated and shown to be enhanced over the value in the extreme quantum limit. 相似文献
18.
19.
By introducing the traffic anticipation effect in the real world into the original lattice hydrodynamic model, we present a new anticipation effect lattice hydrodynamic (AELH) model, and obtain the linear stability condition of the model by applying the linear stability theory. Through nonlinear analysis, we derive the Burgers equation and Korteweg-de Vries (KdV) equation, to describe the propagating behaviour of traffic density waves in the stable and the metastable regions, respectively. The good agreement between simulation results and analytical results shows that the stability of traffic flow can be enhanced when the anticipation effect is considered. 相似文献
20.
BAI Cheng-Lin 《理论物理通讯》2007,48(5):881-884
With the aid of computerized symbolic computation and Riccati equation rational expansion approach, some new and more general rational formal solutions to (2+1)-dimensional Toda system are obtained. The method used here can also be applied to solve other nonlinear differential-difference equation or equations. 相似文献