title: Rational solitons of wave resonant-interaction models.
abstract: Integrable models of resonant interaction of two or more waves in 1+1 dimensions are known to be of applicative interest in several areas. Here we consider a system of three coupled wave equations which includes as special cases the vector nonlinear Schrödinger equations and the equations describing the resonant interaction of three waves. The Darboux-Dressing construction of soliton solutions is applied under the condition that the solutions have rational, or mixed rational-exponential, dependence on coordinates. Our algebraic construction relies on the use of nilpotent matrices and their Jordan form. We systematically search for all bounded rational (mixed rational-exponential) solutions and find a broad family of such solutions of the three wave resonant interaction equations.
authors: INFN, Dipartimento di Fisica, "Sapienza" Università di Roma, P. le A. Moro 2, 00185 Rome, Italy.
authors: Antonio
authors: A
authors: Degasperis
authors: Mathematics and Information Sciences, Northumbria University, Newcastle, United Kingdom.
authors: Sara
authors: S
authors: Lombardo