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Soliton solutions for NLS equation using radial basis functions

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  • Dereli, Yılmaz
  • Irk, Dursun
  • Dağ, İdris

Abstract

We present a numerical study of the cubic nonlinear Schrödinger equation by using the meshless method based on collocation with radial basis functions. The method is examined for the single soliton solution and interaction of two solitons. The results are compared with the analytical solutions given in the literature.

Suggested Citation

  • Dereli, Yılmaz & Irk, Dursun & Dağ, İdris, 2009. "Soliton solutions for NLS equation using radial basis functions," Chaos, Solitons & Fractals, Elsevier, vol. 42(2), pages 1227-1233.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:2:p:1227-1233
    DOI: 10.1016/j.chaos.2009.03.030
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    References listed on IDEAS

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    1. Twizell, E.H. & Bratsos, A.G. & Newby, J.C., 1997. "A finite-difference method for solving the cubic Schrödinger equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 43(1), pages 67-75.
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    Cited by:

    1. Bashan, Ali & Yagmurlu, Nuri Murat & Ucar, Yusuf & Esen, Alaattin, 2017. "An effective approach to numerical soliton solutions for the Schrödinger equation via modified cubic B-spline differential quadrature method," Chaos, Solitons & Fractals, Elsevier, vol. 100(C), pages 45-56.
    2. Korkmaz, Alper, 2018. "Stability satisfied numerical approximates to the non-analytical solutions of the cubic Schrödinger equation," Applied Mathematics and Computation, Elsevier, vol. 331(C), pages 210-231.

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