A chain of connected genes with activation-repression links is analysed. It is shown that for various promoter activity functions (parametrised by Hill coefficient) the equations describing the concentrations of transcription factors are perturbed completely integrable differential-difference of KdV-type. In the case of large Hill coefficient the proteomic signal along the gene network is given...

Considering the Cauchy problem for the modified Korteweg-de Vries-Burgers equation ut + uxxx + ǫ|∂x| u = 2(u)x, u(0) = φ, where 0 < ǫ, α ≤ 1 and u is a real-valued function, we show that it is uniformly globally well-posed in Hs (s ≥ 1) for all ǫ ∈ (0, 1]. Moreover, we prove that for any s ≥ 1 and T > 0, its solution converges in C([0, T ]; Hs) to that of the MKdV equation if ǫ tends to 0.

In this paper, the Homotopy Analysis Method (HAM) is presented for obtaining the approximate solution of new coupled modified Korteweg-de Vries (MKdV) system. The approximate analytical solution is obtained by using this method in the form of a convergent power series with components that are easily computable. For the problems considered, only a few terms are required to obtain an approximate ...

We study the problem of 2-soliton collision for the generalized Korteweg-de Vries equations, completing some recent works of Y. Martel and F. Merle [22, 23]. We classify the nonlinearities for which collisions are elastic or inelastic. Our main result states that in the case of small solitons, with one soliton smaller than the other one, the unique nonlinearities allowing a perfectly elastic co...

امروزه در مبحث محاسبات رآکتورهای هسته‌ای مثل فرسایش و مدیریت سوخت، تحلیل گذرا بازسازی توان میله‌های به دنبال روش‌هایی جهت استفاده کدهای هستند که علاوه بر دقت قابل‌قبول از هزینه زمان بهینه‌ای برخوردار باشند. این پژوهش با گسسته‌سازی معادله پخش نوترون روش نودال بسط شار جریان ‌متوسط مرتبه بالا نشان داده می‌شود روش‌ بهینه قابل‌قبولی بهره می‌برد. مستقیم الحاقی نوترون، برای هندسه مربعی دوبعدی دو گروه ...

We study two members of the multi-component AKNS hierarchy. These are multi-NLS and multi-MKdV systems. derive Hirota bilinear forms these equations obtain soliton solutions. find all possible local nonlocal reductions systems give a prescription to their also (2+1)-dimensional extensions

Abstract In this paper, other types of exact solution of a first-order nonlinear ordinary differential equation is further investigated. By using the solutions of this equation, and a new general ansatz, we give some types of solutions of a class of nonlinear partial differential equations and MKdV equation. These solutions includes solitary wave solutions, singulary solitary solitary solutions...

In this work, we employ the simple direct method to investigate the generalized mKdV equation with variable coefficients. By using this scheme, we found some new exact solutions of the equation, including four new types of Jacobi elliptic function solutions, and these solutions are degenerated to solitary wave solutions and triangle function solutions in the limit case when the modulus of the J...

We extend the action for evolution equations of KdV and MKdV type which was derived in NC] to the case of not periodic, but only equivariant phase space variables, introduced in FV2]. The diierence of these variables may be interpreted as reduced phase space variables via a Marsden-Weinstein reduction where the monodromies play the role of the momentum map. As an example we obtain the doubly di...