Two generalized Harry Dym equations, recently found by Brunelli, Das and Popowicz in the bosonic limit of new supersymmetric extensions of the Harry Dym hierarchy [J. Math. Phys. 44:4756–4767 (2003)], are transformed into previously known integrable systems: one—into a pair of decoupled KdV equations, the other one—into a pair of coupled mKdV equations from a bi-Hamiltonian hierarchy of Kupersh...

The Fibonacci secant function is constructed in this paper. Fibonacci tan-sec method is presented to search for the exact traveling wave solutions of nonlinear differentialdifference equations (DDEs). This method is essentially equivalent to the classical hyperbolic method. The discrete mKdV lattice and some other lattice equations are chosen to illustrate the efficiency and effectiveness of th...

We study a quantum Yang-Baxter structure associated with non-ultralocal lattice models. We discuss the canonical structure of a class of integrable quantum mappings, i.e. canonical transformations preserving the basic commutation relations. As a particular class of solutions we present two examples of quantum mappings associated with the lattice analogues of the KdV and MKdV equations, together...

In this paper, the Exp-function method is used to obtain generalized travelling wave solutions with free parameters of the MKdV-sine-Gordon and Boussinesq-double sine-Gordon equations. It is shown that the Exp-function method, with the help of any symbolic computation packages, provides an effective mathematical tool for nonlinear evolution equations arising in mathematical physics.

In this article we apply the modified extended tanh-function method to find the exact traveling wave solutions of the generalized KdV-mKdV equation with any order nonlinear terms. This method presents a wider applicability for handling many other nonlinear evolution equations in mathematical physics.

We investigate cylindrical and spherical solitons in electron-ion (EI) plasma that contains hot (cold) electrons with stationary ions. The magneto-hydrodynamic equations are solved the aid of reductive perturbation (RP) technique, leading to modified Korteweg–De Vries (mKdV) equation for non-linear behaviour solitary waves EI plasma. By employing reduced differential transform method (RDTM), an...

به کمک شبیه ­سازی دینامیک مولکولی می ­توان تحلیل کوتاه مدت در مقیاس زمانی چند ده پیکوثانیه ­ای را برای مواد آسیب دیده­ی تابشی مورد مطالعه قرار داد. بر همین مبنا این ­سازی، تعداد تعادلی عیوب نقطه بین ­نشین و تهی ­جای مختصات مکانی آن­ها آهن- آلفا دست آورده شد. سپس با استفاده از نتایج حاصل شده، مونت کارلوی جنبشی شیء منظور بررسی تأثیر بازپخت آلفای انجام نشان دادند که یکنواخت دیده­ ی تنها خوشه جای ب...

We analyse an initial-boundary value problem for the mKdV equation on a finite interval by expressing the solution in terms of the solution of an associated matrix Riemann-Hilbert problem in the complex k-plane. This Riemann-Hilbert problem has explicit (x, t)-dependence and it involves certain functions of k referred to as “spectral functions”. Some of these functions are defined in terms of t...

A generalized (G ′ /G)-expansion method is used to search for the exact traveling wave solutions of the coupled KdV-mKdV equation. As a result, some new Jacobi elliptic function solutions are obtained. It is shown that the method is straightforward, concise, effective, and can be used for many other nonlinear evolution equations in mathematical physics.

In this paper, an efficient numerical schemes based on the Haar wavelet method are applied for finding numerical solution of nonlinear third-order modified Korteweg-de Vries (mKdV) equation as well as modified Burgers’ equations. The numerical results are then compared with the exact solutions. The accuracy of the obtained solutions is quite high even if the number of calculation points is small.