2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/127098A certain class of integrable hydrodynamic type systems with three independent and N dependent variables is considered. We choose the existence of a pseudopotential as a criterion of integrability. It turns out that the class of integrable systems having pseudopotentials with movable singularities is described by a functional equation, which can be solved explicitly. This allows us to construct interesting examples of integrable hydrodynamic systems for arbitrary N.12 pages, latexMathematical PhysicsHigh Energy Physics - TheoryQuantum AlgebraExactly Solvable and Integrable Systems17B80, 17B63, 32L81, 14H70text