Communications in Theoretical Physics ›› 2017, Vol. 68 ›› Issue (03): 301-308.

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A Novel Approach with Time-Splitting Spectral Technique for the Coupled Schrödinger-Boussinesq Equations Involving Riesz Fractional Derivative

S. Saha Ray   

  1. Department of Mathematics, National Institute Technology, Rourkela, Orissa-769008, India
  • Received: 2017-04-06 Revised: 2017-05-22 Published: 2017-09-01
  • Funding Information: 

    Supported by NBHM, Mumbai, under Department of Atomic Energy, Government of India vide Grant No. 2/48(7)/2015/NBHM (R.P.)/R&D Ⅱ/11403

Abstract: In the present paper the Riesz fractional coupled Schrödinger-Boussinesq (S-B) equations have been solved by the time-splitting Fourier spectral (TSFS) method. This proposed technique is utilized for discretizing the Schrödinger like equation and further, a pseudospectral discretization has been employed for the Boussinesq-like equation. Apart from that an implicit finite difference approach has also been proposed to compare the results with the solutions obtained from the time-splitting technique. Furthermore, the time-splitting method is proved to be unconditionally stable. The error norms along with the graphical solutions have also been presented here.

Key words: coupled Schrödinger-Boussinesq equations, Riesz fractional derivative, discrete fourier transform, inverse discrete Fourier transform

PACS numbers: 

  • 02.30.Jr