Asymptotic Behavior of the Solution to the Klein–Gordon–Zakharov Model in Dimension Two

Consider the Klein–Gordon–Zakharov equations in $${\mathbb {R}}^{1+2}$$ , and we are interested establishing small global solution to investigating pointwise asymptotic behavior of solution. The can be regarded as a coupled semilinear wave Klein–Gordon system with quadratic nonlinearities which do not satisfy null conditions, fact that components decay sufficiently fast makes it harder conduct analysis. In order conquer difficulties, will rely on hyperboloidal foliation method minor variance ghost weight method. As side result analysis, also able show data existence for class quasilinear violating conditions.