Novel systems of resonant wave interactions. (12th May 2015)

• Record Type: Journal Article
• Authors: Biondini, Gino; Wang, Qiao
• Is Part Of: Journal of physics. Volume 48:Number 22(2015)
• Publication Date: 2015-05-12
• Subjects: Integrable systems -- Lax pair -- dressing method -- Riemann–Hilbert problems -- resonant interactions; Mathematical physics -- Periodicals; Statistical physics -- Periodicals; Quantum theory -- Periodicals; Matter -- Properties -- Periodicals; 530.105
• DOI: 10.1088/1751-8113/48/22/225203
• Languages: English
• ISSNs: 1751-8113

Abstract

Abstract: A matrix Riemann–Hilbert problem (RHP) is constructed using the dressing method starting from two uncoupled, one-directional linear wave equations; the RHP thus obtained is then used to derive a novel integrable matrix non-local system of equations describing resonant wave interactions, together with its Lax pair. This system is shown to be a matrix generalization of the equations for resonant three-wave interactions and stimulated Raman scattering. Several compatible reductions admitted by this system are also discussed.