共查询到20条相似文献,搜索用时 31 毫秒
1.
The hybrid lattice, known as a discrete Korteweg-de Vries (KdV) equation, is found to be a discrete modified Korteweg-de Vries (mKdV) equation in this paper. The coupled hybrid lattice, which is pointed to be a discrete coupled KdV system, is also found to be discrete form of a coupled mKdV systems. Delayed differential reduction system and pure difference systems are derived from the coupled hybrid system by means of the symmetry reduction approach. Cnoidal wave, positon and negaton solutions for the coupled hybrid system are proposed. 相似文献
2.
Nonsingular Travelling Complexiton Solutions to a Coupled Korteweg--de Vries Equation 总被引:1,自引:0,他引:1 下载免费PDF全文
A class of novel nonsingular travelling complexiton solutions to a coupled Korteweg-de Vries (KdV) equation is presented via the first step Darboux transformation of the complex KdV equation with nonzero seed solution. Furthermore, the properties of the nonsingular solutions are discussed. 相似文献
3.
Existence of Formal Conservation Laws of a Variable-Coefficient Korteweg--de Vries Equation from Fluid Dynamics and Plasma Physics via Symbolic Computation 总被引:1,自引:0,他引:1 下载免费PDF全文
Employing the method which can be used to demonstrate the infinite conservation laws for the standard Kortewegde Vries (KdV) equation, we prove that the variable-coeFficient KdV equation under the Painlevé test condition also possesses the formal conservation laws. 相似文献
4.
The coupled semi-discrete modified Korteweg-de Vries equation in (2 1)-dimensions is proposed. It is shown that it can be decomposed into two (1 1)-dimensional differential-difference equations belonging to mKdV lattice hierarchy by considering a discrete isospectral problem. A Darboux transformation is set up for the resulting (2 1)- dimensional lattice soliton equation with the help of gauge transformations of Lax pairs. As an illustration by example,the soliton solutions of the mKdV lattice equation in (2 1)-dimensions are explicitly given. 相似文献
5.
New travelling wave solutions for combined KdV-mKdV equation and (2+1)-dimensional Broer- Kaup- Kupershmidt system 下载免费PDF全文
Some new exact solutions of an auxiliary ordinary differential
equation are obtained, which were neglected by Sirendaoreji {\it et
al in their auxiliary equation method. By using this method and
these new solutions the combined Korteweg--de Vries (KdV) and
modified KdV (mKdV) equation and (2+1)-dimensional
Broer--Kaup--Kupershmidt system are investigated and abundant exact
travelling wave solutions are obtained that include new solitary wave
solutions and triangular periodic wave solutions. 相似文献
6.
H.X. Ge 《Physica A》2009,388(8):1682-1686
The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but is also closely connected with the microscopic car following model. The modified Korteweg-de Vries (mKdV) equation about the density wave in congested traffic has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail in the car following model. So we devote ourselves to obtaining the KdV equation from the lattice hydrodynamic model and obtaining the KdV soliton solution describing the traffic jam. Numerical simulation is conducted, to demonstrate the nonlinear analysis result. 相似文献
7.
In this paper, Lie symmetry is investigated for a new integrable
coupled Korteweg--de Vries (KdV) equation system. Using some symmetry
subalgebra of the equation system, we obtain five types of the
significant similarity reductions. Abundant solutions of the coupled
KdV equation system, such as the solitary wave solution, exponential
solution, rational solution and polynomial solution, etc. are
obtained from the reduced equations. Especially, one type of
group-invariant solution of reduced equations can be acquired by
means of the Painlev\'e I transcendent function. 相似文献
8.
The lattice hydrodynamic model is not only a simplified version of the macroscopic hydrodynamic model, but also connected with the microscopic car following model closely. The modified Korteweg-de Vries (mKdV) equation related to the density wave in a congested traffic region has been derived near the critical point since Nagatani first proposed it. But the Korteweg-de Vries (KdV) equation near the neutral stability line has not been studied, which has been investigated in detail for the car following model. We devote ourselves to obtaining the KdV equation from the original lattice hydrodynamic models and the KdV soliton solution to describe the traffic jam. Especially, we obtain the general soliton solution of the KdV equation and the mKdV equation. We review several lattice hydrodynamic models, which were proposed recently. We compare the modified models and carry out some analysis. Numerical simulations are conducted to demonstrate the nonlinear analysis results. 相似文献
9.
By introducing a flow difference effect, a modified lattice two-lane traffic flow model is proposed, which is proved to be capable of improving the stability of traffic flow. Both the linear stability condition and the kink-antikink solution derived from the modified Korteweg-de Vries (mKdV) equation are analyzed. Numerical simulations verify the theoretical analysis. Furthermore, the evolution laws under different disturbances in the metastable region are studied. 相似文献
10.
A new explicit scheme for the Korteweg~:le Vries (KdV) equation is proposed. The scheme is more stable than the Zabusky Kruskal scheme and the multi-symplectic six-point scheme. When used to simulate the collisions of multi-soliton, it does not show the nonlinear instabilities and un-physical oscillations. 相似文献
11.
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed. 相似文献
12.
In this paper, we study a coupled modified Volterra lattice equation which is an integrable semidiscrete version of the coupled KdV and the coupled mKdV equation. By using the Darboux transformation, we obtain its new explicit solutions including multi-soliton and multi-positon. Furthermore, an integrable discretization of the coupled modified Volterra lattice equation is constructed. 相似文献
13.
A new approach to formulizing a new high-order matrix spectral
problem from a normal 2× 2 matrix modified Korteweg--de Vries
(mKdV) spectral problem is presented. It is found that the
isospectral evolution equation hierarchy of this new higher-order
matrix spectral problem turns out to be the well-known mKdV equation
hierarchy. By using the binary nonlinearization method, a new
integrable decomposition of the mKdV equation is obtained in the
sense of Liouville. The proof of the integrability shows that
r-matrix structure is very interesting. 相似文献
14.
Two velocity difference model for a car following theory 总被引:1,自引:0,他引:1
In the light of the optimal velocity model, a two velocity difference model for a car-following theory is put forward considering navigation in modern traffic. To our knowledge, the model is an improvement over the previous ones theoretically, because it considers more aspects in the car-following process than others. Then we investigate the property of the model using linear and nonlinear analyses. The Korteweg-de Vries equation (for short, the KdV equation) near the neutral stability line and the modified Korteweg-de Vries equation (for short, the mKdV equation) around the critical point are derived by applying the reductive perturbation method. The traffic jam could be thus described by the KdV soliton and the kink-anti-kink soliton for the KdV equation and mKdV equation, respectively. Numerical simulations are made to verify the model, and good results are obtained with the new model. 相似文献
15.
Zhenya Yan 《Physics letters. A》2008,372(7):969-977
In this Letter, the modified Korteweg-de Vries (mKdV) equations with the focusing (+) and defocusing (−) branches are investigated, respectively. Many new types of binary travelling-wave periodic solutions are obtained for the mKdV equation in terms of Jacobi elliptic functions such as sn(ξ,m)cn(ξ,m)dn(ξ,m) and their extensions. Moreover, we analyze asymptotic properties of some solutions. In addition, with the aid of the Miura transformation, we also give the corresponding binary travelling-wave periodic solutions of KdV equation. 相似文献
16.
We propose a simple and direct method for generating travelling wave solutions for nonlinear integrable equations. We illustrate how nontrivial solutions for the KdV, the mKdV and the Boussinesq equations can be obtained from simple solutions of linear equations. We describe how using this method, a soliton solution of the KdV equation can yield soliton solutions for the mKdV as well as the Boussinesq equations. Similarly, starting with cnoidal solutions of the KdV equation, we can obtain the corresponding solutions for the mKdV as well as the Boussinesq equations. Simple solutions of linear equations can also lead to cnoidal solutions of nonlinear systems. Finally, we propose and solve some new families of KdV equations and show how soliton solutions are also obtained for the higher order equations of the KdV hierarchy using this method. 相似文献
17.
We investigate the multisymplectic Euler box scheme for the Korteweg-de Vries (KdV) equation. A new completely explicit six-point scheme is derived. Numerical experiments of the new scheme with comparisons to the Zabusky-Kruskal scheme, the multisymplectic 12-point scheme, the narrow box scheme and the spectral method are made to show nice numerical stability and ability to preserve the integral invariant for long-time integration. 相似文献
18.
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
19.
N-Soliton Solution in Wronskian Form for a Generalized Variable-Coefficient Korteweg--de Vries Equation 下载免费PDF全文
We concentrate on finding exact solutions for a generalized variable-coefficient Korteweg-de Vries equation of physically significance. The analytic N-soliton solution in Wronskian form for such a model is postulated and verified by direct substituting the solution into the bilinear form by virtue of the Wronskian technique. Additionally, the bilinear auto-Backlund transformation between the ( N - 1)- and N-soliton solutions is verified. 相似文献
20.
The Jacobi elliptic function-like exact solutions to two kinds of KdV equations with variable coefficients and KdV equation with forcible term 总被引:3,自引:0,他引:3 下载免费PDF全文
By use of an auxiliary equation and through a function transformation, the Jacobi
elliptic function wave-like solutions, the degenerated soliton-like solutions and
the triangle function wave solutions to two kinds of Korteweg--de Vries (KdV)
equations with variable coefficients and a KdV equation with a forcible term are
constructed with the help of symbolic computation system Mathematica, where the new
solutions are also constructed. 相似文献