Explosive solutions of the three-wave resonant interaction system and their onset from linear instability
Author(s)
Date Issued
May 4, 2026
Type
article
Volume
39
Issue
4
Start Page
Non applicabile
End Page
Non applicabile
Journal
Abstract
The Darboux dressing transformation (DDT) uses known seed solutions to algebraically generate more complex, non-trivial solutions for a nonlinear system. These seeds are frequently modelled as plane waves that constitute the plane wave background upon which subsequent nonlinear structures propagate. We apply the DDT to the three-wave resonant interaction system to derive the analytical expressions for explosive solutions on a plane wave background, along with the formula for their explosion time. We also prove that these solutions exist if their plane wave background is linearly unstable in time, with a gain function that does not vanish at the zero-wavenumber of the perturbation and corresponds to a twisted loop in the stability spectrum.
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