  Two approaches to solution of the two-dimensional Helmholtz equation with a
"wave number" are proposed. The results can be applied both in numerical areas
of physics and in the theory of nonlinear equations. The first approach is
based on the requirement of the covariance of equation under the generalized
Darboux transformation (Moutard transformation). It allows to construct a new
solution of equation, using a given initial solution of the equation.
Simultaneously we obtain the "dressing" relation for the "wave number". The
simplest examples of the approach are considered in detail. In the second
approach the Green-Cauchy formula (the $\bar \partial$-method) is applied to
reduce the solution of the equation to the solution of a system of singular
integral equations.
