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Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials

Received: 12 December 2013     Published: 30 December 2013
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Abstract

In this paper, exact solutions of two-dimensional nonlinear Schrödinger equation with kerr, saturable and quintic type of nonlinearities are studied by means of the Homotopy analysis method (HAM). Linear stability properties of these solutions are investigated by the linearized eigenvalue problem. We also investigate nonlinear stability properties of the exact solutions obtained by HAM by direct simulations.

Published in Applied and Computational Mathematics (Volume 2, Issue 6)
DOI 10.11648/j.acm.20130206.18
Page(s) 152-158
Creative Commons

This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.

Copyright

Copyright © The Author(s), 2013. Published by Science Publishing Group

Keywords

Homotopy Analysis Method, Nonlinear Schrödinger Equation, Stability

References
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[5] Y.Wang, R.Hao, Exact spatial soliton solution for nonlinear Schrödinger equation with a type of transverse non periodic modulation, Optics Communications 282 (2009)3995-3998.
[6] S.Pamuk, N.Pamuk, He’s Homotopy Perturbation Method for continuous population models for single and interacting species, Comp. and Math. with applications 59(2010)612-621.
[7] J.H. He, Homotopy Perturbation Method for Solving Boundary Value Problems, Physics Letters A 350(2006) 87-88.
[8] J.H.He, Recent devolopment of the Homotopy perturbation method, Topological methods in nonlinear analysis, 31(2008)205-209.
[9] Abbasbandy S, The application of Homotopy analysis method to nonlinear equations arising in heat transfer, Physics lett.A,360(2006) 109-13.
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Cite This Article
  • APA Style

    Nalan Antar, Nevin Pamuk. (2013). Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials. Applied and Computational Mathematics, 2(6), 152-158. https://doi.org/10.11648/j.acm.20130206.18

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    ACS Style

    Nalan Antar; Nevin Pamuk. Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials. Appl. Comput. Math. 2013, 2(6), 152-158. doi: 10.11648/j.acm.20130206.18

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    AMA Style

    Nalan Antar, Nevin Pamuk. Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials. Appl Comput Math. 2013;2(6):152-158. doi: 10.11648/j.acm.20130206.18

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  • @article{10.11648/j.acm.20130206.18,
      author = {Nalan Antar and Nevin Pamuk},
      title = {Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials},
      journal = {Applied and Computational Mathematics},
      volume = {2},
      number = {6},
      pages = {152-158},
      doi = {10.11648/j.acm.20130206.18},
      url = {https://doi.org/10.11648/j.acm.20130206.18},
      eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.acm.20130206.18},
      abstract = {In this paper, exact solutions of two-dimensional nonlinear Schrödinger equation with kerr, saturable and quintic type of nonlinearities are studied by means of the Homotopy analysis method (HAM). Linear stability properties of these solutions are investigated by the linearized eigenvalue problem. We also investigate nonlinear stability properties of the exact solutions obtained by HAM by direct simulations.},
     year = {2013}
    }
    

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    T1  - Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials
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    AU  - Nevin Pamuk
    Y1  - 2013/12/30
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    JF  - Applied and Computational Mathematics
    JO  - Applied and Computational Mathematics
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    AB  - In this paper, exact solutions of two-dimensional nonlinear Schrödinger equation with kerr, saturable and quintic type of nonlinearities are studied by means of the Homotopy analysis method (HAM). Linear stability properties of these solutions are investigated by the linearized eigenvalue problem. We also investigate nonlinear stability properties of the exact solutions obtained by HAM by direct simulations.
    VL  - 2
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Author Information
  • Department of Mathematics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey

  • University of Kocaeli, Kocaeli Vocational High School, Kullar, 41300, Kocaeli – TURKEY

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