  Riemann theta functions are used to construct one-periodic and two-periodic
wave solutions to a class of (2+1)-dimensional Hirota bilinear equations. The
basis for the involved solution analysis is the Hirota bilinear formulation,
and the particular dependence of the equations on independent variables
guarantees the existence of one-periodic and two-periodic wave solutions
involving an arbitrary purely imaginary Riemann matrix. The resulting theory is
applied to two nonlinear equations possessing Hirota bilinear forms:
$u_t+u_{xxy}-3uu_y-3u_xv=0$ and $u_t+u_{xxxxy}-(5u_{xx}v+10u_{xy}u-15u^2v)_x=0$
where $v_x=u_y$, thereby yielding their one-periodic and two-periodic wave
solutions describing one dimensional propagation of waves.
