Proof of Maslov's conjecture about the structure of weak point singular solutions of the shallow water equations

We prove Maslov's conjecture that the structure of the type of square root of a quadratic form is the unique structure of weakly singular solutions (w ith a point singularity) of the shallow water equations with the properties of asymptotic self-similarity and stability. This fact plays a key role in the study of the dynamics of vortical singularities and their applications to the description of typhoon trajectories.