共查询到20条相似文献,搜索用时 15 毫秒
1.
Slobodan Zdravković Louis Kavitha Miljko V. Satarić Slobodan Zeković Jovana Petrović 《Chaos, solitons, and fractals》2012,45(11):1378-1386
We here present a model of nonlinear dynamics of microtubules (MT) in the context of modified extended tanh-function (METHF) method. We rely on the ferroelectric model of MTs published earlier by Satari? et al. [1] where the motion of MT subunits is reduced to a single longitudinal degree of freedom per dimer. It is shown that such nonlinear model can lead to existence of kink solitons moving along the MTs. An analytical solution of the basic equation, describing MT dynamics, was compared with the numerical one and a perfect agreement was demonstrated. It is now clearer how the values of the basic parameters of the model, proportional to viscosity and internal electric field, impact MT dynamics. Finally, we offer a possible scenario of how living cells utilize these kinks as signaling tools for regulation of cellular traffic as well as MT depolymerisation. 相似文献
2.
《Chaos, solitons, and fractals》2007,31(4):840-852
Based on computerized symbolic computation and modified extended tanh-function method for constructing a new exact travelling wave solutions of nonlinear evolution equations (NEEs) is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some (NEEs) with mathematical physics interests. As a results, we can successfully recover the previously known solitary wave solutions that had been found by the tanh-function method and other more sophisticated methods. 相似文献
3.
Based on computerized symbolic computation, modified extended tanh-method for constructing multiple travelling wave solutions of nonlinear evolution equations is presented and implemented in a computer algebraic system. Applying this method, with the aid of Maple, we consider some nonlinear evolution equations in mathematical physics such as the nonlinear partial differential equation, nonlinear Fisher-type equation, ZK-BBM equation, generalized Burgers–Fisher equation and Drinfeld–Sokolov system. As a result, we can successfully recover the previously known solitary wave solutions that had been found by the extended tanh-function method and other more sophisticated methods. 相似文献
4.
5.
LIU XiaoJun & GAO Can 《中国科学 数学(英文版)》2011,(2)
In this paper, we solve the extended two-dimensional Toda lattice hierarchy (ex2DTLH) by the generalized dressing method developed in Liu-Lin-Jin-Zeng (2009). General Casoratian determinant solutions for this hierarchy are obtained. In particular, explicit solutions of soliton-type are formulated by using the τ-function in the form of exponential functions. The periodic reduction and one-dimensional reduction of ex2DTLH are studied by finding the constraints. Many reduced systems are shown, including the pe... 相似文献
6.
Dalibor L. Sekuli? Miljko V. Satari?Miloš B. ?ivanov 《Applied mathematics and computation》2011,218(7):3499-3506
By means of computerized symbolic computation and a modified extended tanh-function method the multiple travelling wave solutions of nonlinear partial differential equations is presented and implemented in a computer algebraic system. Applying this method, we consider some of nonlinear partial differential equations of special interest in nanobiosciences and biophysics namely, the transmission line models of microtubules for nano-ionic currents. The nonlinear equations elaborated here are quite original and first proposed in the context of important nanosciences problems related with cell signaling. It could be even of basic importance for explanation of cognitive processes in neurons. As results, we can successfully recover the previously known solitary wave solutions that had been found by other sophisticated methods. The method is straightforward and concise, and it can also be applied to other nonlinear equations in physics. 相似文献
7.
《Chaos, solitons, and fractals》2007,31(3):548-556
In this paper, a new extended Riccati equation rational expansion method is suggested to constructing multiple exact solutions for nonlinear evolution equations. The validity and reliability of the method is tested by its application to the dispersive long wave system and the Broer–Kaup–Kupershmidt system. The method can be applied to other nonlinear evolution equations in mathematical physics. 相似文献
8.
费琪 《纯粹数学与应用数学》2012,(1):109-112
应用双曲函数法结合Riccati方程,求得foam drainage方程的精确解.通过这种方法可以得到此方程的新的孤立波解与周期解,并且此方法可以用来求解其它许多的非线性演化方程. 相似文献
9.
《Chaos, solitons, and fractals》2007,31(1):95-104
By means of a simple transformation technique, we have shown that the higher-order nonlinear Schrödinger equation in nonlinear optical fibers, a new Hamiltonian amplitude equation, generalized Hirota–Satsuma coupled system and generalized ZK-BBM equation can be reduced to the elliptic-like equation. Then, the extended F-expansion method is used to obtain a series of solutions including the single and the combined nondegenerative Jacobi elliptic function solutions and their degenerative solutions to the above mentioned class of nonlinear evolution equations. 相似文献
10.
In this paper,the generalized extended tanh-function method is used for constructing the traveling wave solutions of nonlinear evolution equations.We choose Fisher's equation,the nonlinear schr(o|¨)dinger equation to illustrate the validity and advantages of the method.Many new and more general traveling wave solutions are obtained.Furthermore,this method can also be applied to other nonlinear equations in physics. 相似文献
11.
Generalized method and its application in the higher-order nonlinear Schrodinger equation in nonlinear optical fibres 总被引:8,自引:0,他引:8
A generalized method, which is called the generally projective Riccati equation method, is presented to find more exact solutions of nonlinear differential equations based upon a coupled Riccati equation. As an application of the method, we choose the higher-order nonlinear Schrodinger equation to illustrate the method. As a result more new exact travelling wave solutions are found which include bright soliton solutions, dark soliton solution, new solitary waves, periodic solutions and rational solutions. The new method can be extended to other nonlinear differential equations in mathematical physics. 相似文献
12.
In this paper, an extended simplest equation method is proposed to seek exact travelling wave solutions of nonlinear evolution equations. As applications, many new exact travelling wave solutions for several forms of the fifth-order KdV equation are obtained by using our method. The forms include the Lax, Sawada-Kotera, Sawada-Kotera-Parker-Dye, Caudrey-Dodd-Gibbon, Kaup-Kupershmidt, Kaup-Kupershmidt-Parker-Dye, and the Ito forms. 相似文献
13.
14.
Michael A.B. Deakin 《International Journal of Mathematical Education in Science & Technology》2013,44(3):400-403
An extended Heaviside calculus proposed by Péraire in a recent paper is similar to a generalization of the Laplace transform proposed by the present author. This similarity will be illustrated by analysis of an example supplied by Péraire. 相似文献
15.
V. A. Andreev 《Theoretical and Mathematical Physics》2007,152(3):1286-1298
We use the reduced density matrix of the two-particle spin state to construct a generalized Bell-Clauser-Horne-Shimony-Holt
inequality. For each specific state and under a special choice of the vectors
, this inequality becomes an exact equality. We show how such vectors can be found using the reduced density matrix. Both
sides of this equality have a specific numerical value. We indicate the connection of this number with the measure of entanglement
of the two-particle spin state.
__________
Translated from Teoreticheskaya i Matematicheskaya Fizika, Vol. 152, No. 3, pp. 488–501, September, 2007. 相似文献
16.
《Chaos, solitons, and fractals》2007,31(4):1001-1008
A method to construct the tanh-travelling wave solution of the nonlinear partial differential equations (NPDEs) is present, which combines the two kind methods—the tanh function series method and reduction of the NPDEs to a quadrature problem (RQ method). The nonlinear Schrödinger-type (NLS-type) equations (stable, unstable, inhomogeneous and derivative NLS equations, i.e., SNLS, UNLS, IHNLS and DNLS equations) are chosen to illustrate the method and tanh-travelling wave solutions are obtained. 相似文献
17.
In this paper, firstly, we obtain the variable separation solutions of (2 + 1)-dimensional KdV equation by the extended tanh-function method (ETM) based on mapping method. Novel localized coherent structures about multi-valued functions, i.e. special dromion, special peakon and foldon, and the interactions among them, are discussed. The interactions between two special dromions and between two special peakons possess novel property, that is, there exists a multi-valued foldon in the process of their collision, which is different from the reported cases in previous literature. Moreover, the explicit phase shifts for all the local excitations offered by the quantity u have been given, and are applied to these novel interactions in detail. 相似文献
18.
V. Antony Vijesh P.V. Subrahmanyam 《Journal of Mathematical Analysis and Applications》2008,339(2):1231-1242
In this paper we prove an existence and uniqueness theorem for solving the operator equation F(x)+G(x)=0, where F is a Gateaux differentiable continuous operator while the operator G satisfies a Lipschitz-condition on an open convex subset of a Banach space. As corollaries, a theorem of Tapia on a weak Newton's method and the classical convergence theorem for modified Newton-iterates are deduced. An existence theorem for a generalized Euler-Lagrange equation in the setting of Sobolev space is obtained as a consequence of the main theorem. We also obtain a class of Gateaux differentiable operators which are nowhere Frechet differentiable. Illustrative examples are also provided. 相似文献
19.
20.
The row iterative method is popular in solving the large‐scale ill‐posed problems due to its simplicity and efficiency. In this work we consider the randomized row iterative (RRI) method to tackle this issue. First, we present the semiconvergence analysis of RRI method for the overdetermined and inconsistent system, and derive upper bounds for the noise error propagation in the iteration vectors. To achieve a least squares solution, we then propose an extended version of the RRI (ERRI) method, which in fact can converge in expectation to the solution of the overdetermined or underdetermined, consistent or inconsistent systems. Finally, some numerical examples are given to demonstrate the convergence behaviors of the RRI and ERRI methods for these types of linear system. 相似文献