The purpose of this article is to achieve new soliton solutions the Gilson–Pickering equation (GPE) with assistance Sardar’s subequation method (SSM) and Jacobi elliptic function (JEFM). applications GPE wider because we study some valuable vital equations such as Fornberg–Whitham (FWE), Rosenau–Hyman (RHE) Fuchssteiner–Fokas–Camassa–Holm (FFCHE) obtained by particular choices parameters involv...

We present a systematic approach for calculating higher-order derivatives of smooth functions on a uniform grid using Padé approximants. We illustrate our findings by deriving higher-order approximations using traditional second-order finite-difference formulas as our starting point. We employ these schemes to study the stability and dynamical properties of K(2,2) Rosenau-Hyman compactons inclu...

We prove a comparison theorem for the isoperimetric profiles of solutions of the normalized Ricci flow on the two-sphere: If the isoperimetric profile of the initial metric is greater than that of some positively curved axisymmetric metric, then the inequality remains true for the isoperimetric profiles of the evolved metrics. We apply this using the Rosenau solution as the model metric to dedu...

We study the cubic ab-family of equations, which includes both Fokas-Olver-Rosenau-Qiao (FORQ) and Novikov (NE) equations. For a≠0, it is proved that there exist initial data in Sobolev space Hs, s<3/2, with nonunique solutions. Multiple solutions are constructed by studying collision 2-peakon Furthermore, we prove novel phenomenon for some members family, between 2-peakons can occur even if “f...

A selection of these reports is available in PostScript form at the Faculty's anonymous ftp-Abstract We study the large-time behaviour and the behaviour of the interfaces of the nonlinear diiusion equation (x)u t = A(u) in one and two space dimensions. The function A is of porous media type, smooth but with a vanishing derivative at some values of u, and > 0 is supposed continuous and bounded f...

which has been studied in detail by P. Rosenau and J.M. Hyman [2]. In the literature there are many studies dealing with the travelling wave solutions of the K(m,n) and B(m,n) equations, but in general they are restricted to the case m = n [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14]. When m 6= n, the solutions of K(m,n) were investigated in [2, 3]. Our aim here is just to search for solutions ...

The third-order nonlinear dispersion PDE, as the key model, (0.1) ut = (uux)xx in R × R+, is studied. Two Riemann’s problems for (0.1) with initial data S∓(x) = ∓signx, create the shock (u(x, t) ≡ S−(x)) and smooth rarefaction (for data S+) waves, [18]. The concept of “δ-entropy” solutions (a“δ-entropy test”) and others are developed for distinguishing shock and rarefaction waves by using stabl...

We study the large-time behaviour and the behaviour of the interfaces of the non-linear diiusion equation (x)u t = A(u) in one and two space dimensions. The function A is of porous media type, smooth but with a vanishing derivative at some values of u, and > 0 is supposed continuous and bounded from above. If is not bounded away from zero, the large-time behaviour of solutions and their interfa...