New extended generalized Kudryashov method for solving three nonlinear partial differential equations

New extended generalized Kudryashov method is proposed in this paper for the first time. Many solitons and other solutions of three nonlinear partial differential equations (PDEs), namely, the (1+1)-dimensional improved perturbed nonlinear Schrödinger equation with anti-cubic nonlinearity, the (2+1)-dimensional Davey–Sterwatson (DS) equation and the (3+1)-dimensional modified Zakharov–Kuznetsov (mZK) equation of ion-acoustic waves in a magnetized plasma have been presented. Comparing our new results with the well-known results are given. Our results in this article emphasize that the used method gives a vast applicability for handling other nonlinear partial differential equations in mathematical physics

Nonlinear structures: explosive, soliton and shock in a quantum electron-positron-ion magnetoplasma

Theoretical and numerical studies are performed for the nonlinear structures (explosive, solitons and shock) in quantum electron-positron-ion magnetoplasmas. For this purpose, the reductive perturbation method is employed to the quantum hydrodynamical equations and the Poisson equation, obtaining extended quantum Zakharov-Kuznetsov equation. The latter has been solved using the generalized expansion method to obtain a set of analytical solutions, which reflect the possibility of the propagation of various nonlinear structures. The relevance of the present investigation to the white dwarfs is highlighted.Comment: 7 figure

Asymptotic behavior for a class of solutions to the critical modified Zakharov-Kuznetsov equation

We consider the initial value problem (IVP) associated to the modified Zakharov-Kuznetsov (mZK) equation \begin{equation}\nonumber u_t+6u^2u_x+u_{xxx}+u_{xyy}=0, \quad (x,y)\in \mathbb{R}^2, \; t \in \mathbb{R}, \end{equation} which is known to have global solution for given data in $u(x,y,0) = u_0(x,y)\in H^1(\mathbb{R}^2)$ satisfying $\|u_0\|_{L^2} <\sqrt{3} \|\phi\|_{L^2}$, where $\phi$ is a solitary wave solution. In this work, the issue of the asymptotic behavior of the solutions of the modified Zakharov-Kuznetsov equation with negative energy is addressed. The principal tool to obtain the main result is the use of appropriate scaling argument from Angulo et al [4, 5].FC