2017/03/28 by Xiaoyu Ding, Ding, X., Soohyeon Kang +1
Computer Science · Mathematics · Physics and Astronomy · #65D30 #65P20 #65Z05 #Advanced Fiber Laser Technologies #Computational Physics (physics.comp-ph) #FOS: Physical sciences #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.1703.09622
openalex publication_date 2017/03/28 · openalex created_date 2017/11/10 · openalex updated_date 2026/07/28
This paper is a survey on exponential integrators to solve cubic-quintic complex Ginzburg-Landau equations and related stiff problems. In particular, we are interested in accurate computation near the pulsating and exploding soliton solutions where different time scales exist. We explore stepsize-adaptive variations of three types of exponential integrators: integrating factor (IF) methods, exponential Runge-Kutta (ERK) methods and split-step (SS) methods, and their embedded versions for computation and comparison. We present the details, derive formulas for completeness, and consider seven different stepsize-adaptive integrating schemes to solve the cubic-quintic complex Ginzburg-Landau equation. Moreover, we propose using a comoving frame to resolve fast phase rotation for better performance. We present thorough comparisons and experiments in the one- and two-dimensional cubic-quintic complex Ginzburg-Landau equations.