Skip to main content
Mass Conservative Method for Solving the Fractional Nonlinear Schrödinger Equation
Computers & Mathematics with Applications
  • Siwei Duo
  • Yanzhi Zhang, Missouri University of Science and Technology

We propose three Fourier spectral methods, i.e., the split-step Fourier spectral (SSFS), the Crank–Nicolson Fourier spectral (CNFS), and the relaxation Fourier spectral (ReFS) methods, for solving the fractional nonlinear Schrödinger (NLS) equation. All of them are mass conservative and time reversible, and they have the spectral order accuracy in space and the second-order accuracy in time. In addition, the CNFS and ReFS methods are energy conservative. The performance of these methods in simulating the plane wave and soliton dynamics is discussed. The SSFS method preserves the dispersion relation, and thus it is more accurate for studying the long-time behaviors of the plane wave solutions. Furthermore, our numerical simulations suggest that the SSFS method is better in solving the defocusing NLS, but the CNFS and ReFS methods are more effective for the focusing NLS.

Mathematics and Statistics
Research Center/Lab(s)
Center for High Performance Computing Research
Document Type
Article - Journal
Document Version
File Type
© 2016 Elsevier, All rights reserved.
Publication Date
Citation Information
Siwei Duo and Yanzhi Zhang. "Mass Conservative Method for Solving the Fractional Nonlinear Schrödinger Equation" Computers & Mathematics with Applications Vol. 71 (2016) p. 2257 - 2271
Available at: