In this paper we discuss the algebraic construction of the mKdV hierarchy in terms of an affine Lie algebra ŝl(2). An interesting novelty araises from the negative even grade sector of the affine algebra leading to nonlinear integro-differential equations admiting non-trivial vacuum configuration. These solitons solutions are constructed systematically from generalization of the dressing method...

In this paper, the variational iteration method (VIM) is reintroduced with Laplace transforms and the Padé technique treatment to obtain closed form solutions of nonlinear equations. Some examples, including the coupled Burger’s equation, compacton k(n, n) equation, Zakharov–Kuznetsov Zk(n, n) equation, and KdV and mKdV equations are given to show the effectiveness of the coupled VIM–Laplace–Pa...

In this paper, we discuss the Hamiltonian structure of Korteweg–de Vries equation, modified Korteweg–de Vries equation, and generalized Korteweg– de Vries equation. We proposed the Sine-function algorithm to obtain the exact solution for non-linear partial differential equations. This method is used to obtain the exact solutions for KdV, mKdV and GKdV equations. Also, we have applied the method...

Quaternionic vector mKDV equations are derived from the Cartan structure equation in the symmetric space n =Sp(n+ 1)/Sp(1)×Sp(n). The derivation of the soliton hierarchy utilizes a moving parallel frame and a Cartan connection 1-form ω related to the Cartan geometry on n modelled on (spn+1, sp1 × spn). The integrability structure is shown to be geometrically encoded by a Poisson– Nijenhuis stru...

In the past three decades, traveling wave solutions to the Korteweg–de Vries equation have been studied extensively and a large number of theoretical issues concerning the KdV equation have received considerable attention. These wave solutions when they exist can enable us to well understand the mechanism of the complicated physical phenomena and dynamical processes modeled by these nonlinear e...

In this article we continue to develop the theory of generating symmetries for integrable equations. A technique computation using Maple is presented. The based on standard symmetry method. By it find KdV, Camassa–Holm, mKdV, sine-Gordon, Boussinesq, associated Degasperis-Procesi and Novikov

A bi-Hamiltonian hierarchy of quaternion soliton equations is derived from geometric non-stretching flows of curves in the quaternionic projective space HPn. The derivation adapts the method and results in recent work by one of us on the Hamiltonian structure of non-stretching curve flows in Riemannian symmetric spaces M = G/H by viewing HPn ≃ U(n + 1, H)/U(1, H)× U(n, H) ≃ Sp(n + 1)/Sp(1)× Sp(...

هدف: این پژوهش با هدف آزمون مدل روابط بین سبک‌های مقابله و خودکارآمدی حرفه‌ای استرس ادراک شده ناشی از حرفه‌های سلامت در گروهی پرستاران انجام شد. روش: همبستگی، 151 نفر شاغل بخش‌های اونکولوژی دانشگاه علوم پزشکی تهران به پرسشنامه باورهای شغلی برای (پیسانتی، لامباردو، لوسیدی، لازاری برتینی، 2008)، نسخة کوتاه سیاهه موقعیت‌های استرس‌زا (کوهن، جانگ استین، 2006) (ولفگانگ، 1988) پاسخ دادند. مفروض روش آم...