Efficient energy‐preserving scheme of the three‐coupled nonlinear Schrödinger equation. (21st March 2019)

• Record Type: Journal Article
• Authors: Kong, Linghua; Wei, Ping; Hong, Yuqi; Zhang, Peng; Wang, Ping
• Is Part Of: Mathematical methods in the applied sciences. Volume 42:Number 9(2019)
• Page Start: 3222
• Page End: 3235
• Publication Date: 2019-03-21
• Subjects: averaged vector field method -- conservation laws -- high‐order compact method -- three‐coupled nonlinear Schrödinger equation; Mathematics -- Periodicals; Technology -- Mathematics -- Periodicals; 519
• DOI: 10.1002/mma.5580
• Languages: English
• ISSNs: 0170-4214

Abstract

Abstract : An energy‐preserving scheme is proposed for the three‐coupled nonlinear Schrödinger (T‐CNLS) equation. The T‐CNLS equation is rewritten into the classical Hamiltonian form. Then the spatial variable is discretized by using high‐order compact method to convert it into a finite‐dimensional Hamiltonian system. Next, a second‐order averaged vector field (AVF) method is employed in time which results in an energy‐preserving scheme. Some theoretical results such as convergence are investigated. In addition, it provides some numerical examples to illustrate the robustness and reliability of the theoretical results. It also explores the role of the parameters in the model and initial condition on the wave propagation.