2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/79773We discuss the integrability properties of the Boussinesq equations in the language of geometrical quantities defined on an appropriately chosen coset manifold connected with the $W_{3}$ algebra of Zamolodchikov. We provide a geometrical interpretation to the commuting conserved quantities, Lax-pair formulation, zero-curvature representation, Miura maps, etc. in the framework of nonlinear realization method.LaTeX, 10 pagesExactly Solvable and Integrable SystemsHigh Energy Physics - TheoryMathematical Physicstext