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A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations

Author

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  • Ömer Oruç

    (Department of Mathematics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey)

  • Alaattin Esen

    (Department of Mathematics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey)

  • Fatih Bulut

    (Department of Physics, Faculty of Arts and Science, Inonu University, 44280 Malatya, Turkey)

Abstract

In this paper, to obtain accurate numerical solutions of coupled nonlinear Schrödinger–Korteweg-de Vries (KdV) equations a Haar wavelet collocation method is proposed. An explicit time stepping scheme is used for discretization of time derivatives and nonlinear terms that appeared in the equations are linearized by a linearization technique and space derivatives are discretized by Haar wavelets. In order to test the accuracy and reliability of the proposed method L2, L∞ error norms and conserved quantities are used. Also obtained results are compared with previous ones obtained by finite element method, Crank–Nicolson method and radial basis function meshless methods. Error analysis of Haar wavelets is also given.

Suggested Citation

  • Ömer Oruç & Alaattin Esen & Fatih Bulut, 2016. "A Haar wavelet collocation method for coupled nonlinear Schrödinger–KdV equations," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 27(09), pages 1-16, September.
    • Handle: RePEc:wsi:ijmpcx:v:27:y:2016:i:09:n:s0129183116501035
    DOI: 10.1142/S0129183116501035
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    Citations

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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. Pathak, Maheshwar & Joshi, Pratibha & Nisar, Kottakkaran Sooppy, 2022. "Numerical study of generalized 2-D nonlinear Schrödinger equation using Kansa method," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 200(C), pages 186-198.
    3. Li, Jiyong, 2021. "Convergence analysis of a symmetric exponential integrator Fourier pseudo-spectral scheme for the Klein–Gordon–Dirac equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 190(C), pages 691-713.
    4. Bulut, Fatih & Oruç, Ömer & Esen, Alaattin, 2022. "Higher order Haar wavelet method integrated with strang splitting for solving regularized long wave equation," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 197(C), pages 277-290.
    5. Huang, Yifei & Peng, Gang & Zhang, Gengen & Zhang, Hong, 2023. "High-order Runge–Kutta structure-preserving methods for the coupled nonlinear Schrödinger–KdV equations," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 208(C), pages 603-618.
    6. Pervaiz, Nosheen & Aziz, Imran, 2020. "Haar wavelet approximation for the solution of cubic nonlinear Schrodinger equations," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).

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