The head-on collision between two-counter-propagating electron acoustic solitons and double layers (DLs) in an unmagnetized collisionless multi-species plasma consisting of inertial cold fluid (α, q)-distributed hot electrons positrons has been analyzed with the stationary background massive positive ions. For nonlinear analysis colliding wave phenomena, coupled Korteweg–de Vries equation (KdVE...

Abstract We prove local existence and uniqueness of solutions of the focusing modified Korteweg de Vries equation ut+u 2 ux+uxxx = 0 in classes of unbounded functions that admit an asymptotic expansion at infinity in decreasing powers of x. We show that an asymptotic solution differs from a genuine solution by a smooth function that is of Schwartz class with respect to x and that solves a gener...

In this paper, an algorithm is presented to find exact polynomial solutions of nonlinear differential-difference equations(DDEs) in terms of the Jacobi elliptic functions. The key steps of the algorithm are illustrated by the discretized mKdV lattice. A Maple package JACOBI is developed based on the algorithm to automatically compute special solutions of nonlinear DDEs. The effectiveness of the...

— In this paper we give an algorithmic method of deriving the Lax pair for the modified Korteweg-de Vries hierarchy. For each n, the compatibility condition gives the n-th member of the hierarchy, rather than its derivative. A direct consequence of this is that we obtain the isomonodromy problem for the second Painlevé hierarchy, which is derived through a scaling reduction. Résumé (La paire de...

The inverse scattering transform allows explicit construction of solutions to many physically significant nonlinear wave equations. Notably, this method can be extended fractional evolution equations characterized by anomalous dispersion using completeness suitable eigenfunctions the associated linear problem. In diffusion, mean squared displacement is proportional $t^{\alpha}$, $\alpha>0$, whi...

به‌منظور تحلیل نوترونیک قلب رآکتورها، نیاز به توسعه نرم‌افزارهای محاسبات هسته‌ای جهت تولید ثابت‌های چند گروهی و حل عددی معادله پخش است. برای این منظور، از روش‌هایی استفاده می‌شود که علاوه بر دقت مناسب حجم زمان بهینه‌ای برخوردار باشند. در پژوهش تئوری حاکم روش نودال بسط شار جریان متوسط هم‌چنین مرتبه‌های بالاتر پرداخته می‌شود. پس‌ازآن با گسسته‌سازی نوترون، نشان داده روش‌ بهینه خوبی بهره می‌برد. مس...

Self-localized modes in a quantum vibronic system, with long range interaction of Kac-Baker type and interacting nonlinearly with an acoustical phonon bath, is studied. One works in the coherent state approximation. Following a procedure of Sarker and Krumhansl the problem is reduced to a nearest neighbours one. In the continuum limit the localized state satisfy a mKdV equation. An approximate ...

By using solutions of an ordinary differential equation, an auxiliary equation method is described to seek exact solutions of nonlinear evolution equations with variable coefficients. Being concise and straightforward, this method is applied to the mKdV equation with variable coefficients. As a result, new explicit solutions including solitary wave solutions and trigonometric function solutions...

We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which inc...

Abstract: In this paper, the Exp-function method with the aid of symbolic computational system is used to obtain generalized solitary solutions and periodic solutions of the MKdV equation, Burgers’ equation in one and two dimensional with variable coefficients. It is shown that the Exp-function method, with the help of symbolic computation, provides a powerful mathematical tool for solving othe...