2021/03/26 by David Juhasz, Juhasz, David, Per Kristen Jakobsen +1
Computer Science · Mathematics · Physics and Astronomy · #Computational Physics (physics.comp-ph) #FOS: Mathematics #FOS: Physical sciences #Numerical Analysis (math.NA) #Pattern Formation and Solitons (nlin.PS) #cs.NA #math.NA #nlin.PS #physics.comp-ph
paper · pdf · doi:10.48550/arxiv.2103.14437
arxiv created 2021/03/26 · arxiv updated 2021/03/29
In this paper we study dispersive wave equation using the method of multiple scales (MMS) and perform several numerical tests to investigate its accuracy. The key feature of our MMS solution is the linearity of the amplitude equation and the complex nature of the time-frequency. The MMS is tested as an initial value problem using three choices of the dispersion model, one toy and two Lorentz models. Depending on the parameters of the problem, the amplitude equation can be both well- or ill-posed. Despite the ill-posedness, the MMS solution remains a valid approximation of the solution to the original nonlinear model.