turkmath.org

The N-coupled nonlinear Schrödinger (N-CNLS) equation arises as the governing model equation in several branches of physics including, for example, optics, fluid dynamics, quantum mechanics and biophysics (cf. [1-3] and references therein). In the last decades, there has been an increased interest in numerical preservation of one or more physical/geometric properties of the mechanical system under consideration [4, 5]. In this study, we construct an energy conserving numerical scheme for the 3-CNLS equation by using the AVF method [6, 7]. Many numerical results are carried out to test the efficiency and reliability of the proposed scheme for the 3-CNLS equation. The numerical results show that the proposed energy conserving scheme has an excellent performance in simulating the plane wave, periodic, single and colliding soliton solutions of the 3-CNLS equation during long-time integration. The ability of capturing low- and high-frequency waves is examined for the proposed scheme. Moreover, the scheme preserves the other invariants of the 3-CNLS equation as well as the discrete energy of the system. (joint work with Sevim Ertuğ)