In this paper, we consider questions of inner regularity weak solutions initial-boundary value problems for the Zakharov–Kuznetsov equation with two spatial variables. The initial function is assumed to be irregular, and main parameter governing decay rate at infinity. results paper are obtained problem on a half-strip. problem, different types conditions (e.g., Dirichlet or Neumann conditions)...

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.

The   ) ( exp    -expansion method is a promising method for finding exact traveling wave solutions to nonlinear evolution equations in physical sciences. In this article, we use the   ) ( exp    -expansion method to find the exact solutions for the nonlinear Zakharov-Kuznetsov-Benjamin-Bona-Mahony equation and the good Boussinesq equations. Many solitary wave solutions are formally d...

We solve the group classification problem for $2+1$ generalized quantum Zakharov-Kuznetsov equation. Particularly we consider equation $u_{t}+f\left( u\right) u_{z}+u_{zzz}+u_{xxz}=0$, and time-dependent $u_{t}+\delta \left( t\right) uu_{z}+\lambda u_{zzz}+\varepsilon u_{xxz}=0$% . Function $f\left( $ $\delta ,~\lambda $,~$\varepsilon are determine in order equations to admit additional Lie sym...