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applied math seminar

Event Type: 
Seminar
Speaker: 
Alexander Korotkevich, Department of Math&Stat, UNM
Event Date: 
Monday, August 30, 2021 -
3:30pm to 4:30pm
Location: 
Zoom Meeting https://unm.zoom.us/j/92530807006
Audience: 
General PublicFaculty/StaffStudentsAlumni/Friends
Sponsor/s: 
Pavel Lushnikov

Event Description: 

Speaker: Alexander  Korotkevich (UNM)

Event Date: Monday, 3:30pm Aug 30, 2021

Location: Zoom Meeting

Title: Direct Numerical Validation of 6-Wave 1D Kinetic Equation

Abstract:
We consider wave kinetic equation (WKE) for quintic nonlinear Schroedinger equation (qNLSE),
corresponding to 6-waves 3-to-3 interaction. WKE was derived for periodic boundary conditions. We
propose conditions of applicability of WKE for description of qNLSE. This conditions were confirmed
during comparison of simulation of dynamical equation (qNLSE) and WKE. We observed convergence of
solution of qNLSE to solution of WKE with increase of the period of the system. If we stay in
proposed range of applicability, good correspondence between WKE and qNLSE is observed.

6-waves qNLSE appears in some of the applications, e.g. if one considers one dimensional optical
fiber communication line and would like to consider turbulence of the waves propagating in it. Next
order correction on intensity, with respect to the classical NLSE, would result in qNLSE, after
canonical transformation eliminating 4-waves nonlinear term. Also 6-waves WKE appears in description
of waves on Kelvin vortices.