In this paper, we propose the fractal (2 + 1)-dimensional Zakharov–Kuznetsov equation based on He’s derivative for first time. The generalized variational formulation is established by using semi-inverse method and two-scale theory. obtained principle important since it not only reveals structure of traveling wave solutions but also helps us study symmetric finding paper will contribute to symm...

Further extension of the generalized and improved (G0/G)-expansion method; Nonlinear ordinary differential equation; ZKBBM equation; Travelling wave solutions Abstract In this article, the generalized and improved (G0/G)-expansion method has been proposed for further extension to generate many new travelling wave solutions. In addition, nonlinear ordinary differential equation is implemented as...

Dimension breaking occurs when the solution of a nonlinear partial differential equation (PDE) depending on n independent variables bifurcates to one depending on n + 1. A central hypothesis in the theory of dimension breaking is that a certain operator should have a non-zero purely imaginary eigenvalue. This hypothesis is difficult to verify in general. We present a geometric theory for verify...

This paper is concerned with the Cauchy problem of modified Zakharov-Kuznetsov equation on $\mathbb{R}^d$. If $d=2$, we prove sharp estimate which implies local in time well-posedness Sobolev space $H^s(\mathbb{R}^2)$ for $s \geq 1/4$. $d 3$, by employing $U^p$ and $V^p$ spaces, establish small data global scaling critical $H^{s_c}(\mathbb{R}^d)$ where $s_c = d/2-1$.