Rational solutions of the classical Boussinesq system

Rational solutions of the classical Boussinesq system are expressed in terms of special polynomials associated with rational solutions of the fourth Painlevé equation, which arises as a scaling reduction of the classical Boussinesq system. Generalized rational solutions of the classical Boussinesq system, which involve an infinite number of arbitrary constants, are also derived. The generalized rational solutions are analogues of such solutions for the Korteweg–de Vries, Boussinesq and nonlinear Schrödinger equations.