  In this study, we present non-linear spin wave analysis of a quasi 2D
spin-$\frac{1}{2}$ $J_1-J_2$ antiferromagnet at the parameter regime relevant
for the recently studied compound $Zn_2VO(PO_4)_2$. We obtain the temperature
dependence of the spin wave energy, susceptibility and magnetization using
Green's function technique and Hartree-Fock factorization or Tyablikov's
decoupling approximation. The comparison of our numerical results with the
experimental findings is discussed. Magnetic structure factor is calculated and
compared with powder neutron diffraction data. We also study the spin wave
behavior of the compound $Zn_2Ti_{0.25}V_{0.75}O(PO_4)_2$ obtained by partial
chemical substitution of $Ti$ at $V$ sites of the compound $Zn_2VO(PO_4)_2$
(Phys. Rev. B87, 054431). Due to the superlattice structure of the spin
lattice, the substituted compound possess multiple spin wave modes. The spin
wave analysis confirms the quasi-1D nature of the substituted system.
