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 Γ 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