Real finite-gap regular solutions of the Kaup-Boussinesq equation (Q1089838)

All the solutions of the Kaup-Boussinesq equation with a finite number of gaps are known in terms of Riemann theta-functions [\textit{V. B. Matveev} and \textit{M. I. Yavor}, Ann. Inst. Henri Poincaré, Nouv. Ser., Sect. A 31, 25-41 (1979; Zbl 0435.76016)]. Here, the real regular finite gap solutions of the Kaup-Boussinesq equation are singled out and described. Moreover the solutions with two or three gaps are written down (using a theorem of Appel) in terms of the one-dimensional theta functions.