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)...

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...

The natural transform decomposition method (NTDM) is a relatively new transformation for finding an approximate differential equation solution. In the current study, NTDM has been used obtaining solution of fractional-order generalized perturbed Zakharov–Kuznetsov (GPZK) equation. tested three nonlinear cases GPZK absolute errors are analyzed by proposed and q-homotopy analysis (q-HATM). 3D 2D ...

we apply the improved G′/G -expansion method for constructing abundant new exact traveling wave solutions of the 2 1 -dimensional Modified Zakharov-Kuznetsov equation. In addition, G ′′ λG′ μG 0 together with b α ∑w q −w pq G ′/G q is employed in this method, where pq q 0,±1,±2, . . . ,±w , λ and μ are constants. Moreover, the obtained solutions including solitons and periodic solutions are des...

a r t i c l e i n f o a b s t r a c t Initial–boundary value problems for the linear 2D Zakharov–Kuznetsov equation posed on bounded rectangles and on a channel-like strip are considered. We suggest a condition on a part of the boundary such that the evolution problem posed on a bounded rectangle has no critical restrictions on its size. The similar results are obtained both for a 2D strip and ...