Abstract The main purpose here is the study of dispersive blow-up for solutions Zakharov-Kuznetsov equation. Dispersive refers to point singularities due focusing short or long waves. We will construct initial data such that linear problem present this kind singularities. Then we show corresponding nonlinear inherited from component part Similar results are obtained generalized

In this paper an approximate analytical solution of the fractional Zakharov-Kuznetsov equations will be obtained with the help of the reduced differential transform method (RDTM). It is in-dicated that the solutions obtained by the RDTM are reliable and present an effective method for strongly nonlinear fractional partial differential equations.

We prove that the initial value problem for the two-dimensional modified ZakharovKuznetsov equation is locally well-posed for data in H(R), s > 3/4. Even though the critical space for this equation is L(R) we prove that well-posedness is not possible in such space. Global well-posedness and a sharp maximal function estimate are also established.

Transverse instabilities correspond to a class of perturbations traveling in a direction transverse to the direction of the basic solitary wave. Solitary waves traveling in one space direction generally come in one-parameter families. We embed them in a two-parameter family and deduce a new geometric condition for transverse instability of solitary waves. This condition is universal in the sens...

The main idea of this paper is to study the chaotic behavior Zakharov–Kuznetsov equation with perturbation. By taking traveling wave transformation, we transform perturbed dual-power law and triple-power nonlinearity into planar dynamic systems, then analyze how external terms affect behavior. We emphasize here that there no phenomenon for non-perturbed ZK equation, thus it only caused by terms.

In this paper, the (2+1)-dimensional extended quantum Zakharov-Kuznetsov equation is further explored. The shown to be self-adjoint and conserved vector constructed according related theorem. Then corresponding optimal system of one-dimensional subgroups determined. Similarity reductions under are performed. As a result, reduced into linear PDE with two independent variables.