Exact solutions of the 3-wave resonant interaction equation

Details Exact solutions of the 3-wave resonant interaction equation Exact solutions of the 3-wave resonant interaction equation

2005-09-21

arxiv.org/abs/nlin/0509038v1

Nonlinear Sciences

Exactly Solvable and Integrable Systems

15 pages, 9 figures, standard LaTeX2e, submitted for publication to Physica D

Scientific paper

The Darboux--Dressing Transformations are applied to the Lax pair associated to the system of nonlinear equations describing the resonant interaction of three waves in 1+1 dimensions. We display explicit solutions featuring localized waves whose profile vanishes at the spacial boundary plus and minus infinity, and which are not pure soliton solutions. These solutions depend on an arbitrary function and allow to deal with collisions of waves with various profiles.

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