Two-gap elliptic solutions of the Boussinesq equation

Two-gap solutions of the Boussinesq equation are considered. It is shown that for almost every Riemann surface $\Gamma$ of genus $g=2$ covering the elliptic surface it is possible to construct an elliptic (in $x$) two-gap solution of the Boussinesq equation. The existence of third- and fourth-order differential operators with elliptic “two-gap” potentials having an arbitrary number of poles is also established. An example is given.