New coupled Liouville system: Prolongation structure, soliton solution, and complete integrability (Q1825381)

The authors investigate a coupled version of a Liouville equation which may play some role in the theory of nonlinear equations in two dimensions. Utilizing the technique of prolongation of Lie algebras, the authors derive the Lax pair and the closure of the prolongation algebra. The scaling invariance is noted. Explicit soliton solutions are found. The authors prove the complete integrability of the system, using Painlevé's criterion advocated by Ablowitz. The level of rigor is the level acceptable in theoretical physics.