In this paper, we propose and study two time-splitting spectral methods for the generalized Zakharov system. These methods are spectrally accurate in space, second order in time, and unconditionally stable. The unconditional stability of the methods offers greater numerical efficiency than those given in previous papers, especially in the subsonic regime. Our numerical experiments confirm the a...

We introduce the notion of generalized Darboux-Manakov-Zakharov systems of semilinear partial differential equations. ∂ 2u ∂xi∂x j = fi j ( xk,u, ∂u ∂xl ) , 1 ≤ i < j ≤ n, k, l ∈ {1, . . . ,n}. (1) for a real-valued function u(x1, . . . ,xn). These generalize linear systems in the equation class ∂ 2u ∂xi∂x j −Γ j i(x) ∂u ∂xi −Γi j(x) ∂u ∂x j +C(i j)(x)u = 0, 1 ≤ i < j ≤ n, (2) where coefficient...

Bäcklund transformations, which are relations among solutions of partial differential equations–usually nonlinear–have been found and applied mainly for systems with two independent variables. A few are known for equations like the Kadomtsev-Petviashvili equation [1], which has three independent variables, but they are rare. Wahlquist and Estabrook [2] discovered a systematic method for searchi...

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.