Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials
Applied and Computational Mathematics
Volume 2, Issue 6, December 2013, Pages: 152-158
Received: Dec. 12, 2013;
Published: Dec. 30, 2013
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Nalan Antar, Department of Mathematics, Istanbul Technical University, Maslak 34469, Istanbul, Turkey
Nevin Pamuk, University of Kocaeli, Kocaeli Vocational High School, Kullar, 41300, Kocaeli – TURKEY
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.
Exact Solutions of two-Dimensional Nonlinear Schrödinger Equations with External Potentials, Applied and Computational Mathematics.
Vol. 2, No. 6,
2013, pp. 152-158.
S.J.Liao, The proposed homotopy analysis technique for the solution of nonlinear problems, Ph.D thesis, Shanghai Jiao tong University, (1992)
J.H.He, Homotopy perturbation technique, Comput.Methods Appl. Mech.Engrg 178(1999) 257-262.
J.H.He, Homotopy perturbation method. A new nonlinear analytical Technique, Appl.Math.Comp. 135(2003)73-79.
N.Pamuk, Series Solution for Porous Medium Equation with a Source Term by Adomian’s Decomposition Method, Appl. Math.Comput.178(2006)480-485.
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.
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.
J.H. He, Homotopy Perturbation Method for Solving Boundary Value Problems, Physics Letters A 350(2006) 87-88.
J.H.He, Recent devolopment of the Homotopy perturbation method, Topological methods in nonlinear analysis, 31(2008)205-209.
Abbasbandy S, The application of Homotopy analysis method to nonlinear equations arising in heat transfer, Physics lett.A,360(2006) 109-13.
Liao SJ, On the Homotopy analysis method for nonlinear problems, Appl. math.comp., 147(2004)499-513.
Liao SJ, Numerically solving nonlinear problems by Homotopy analysis method, Comput.mech., 20(1997)530-40.
J.H.He, Comparison of Homotopy perturbation method and homotopy analysis method, Applied Math. and comp.,156(2004) 527-539.
J.H.He, An elementary introduction to the homotopy perturbation method, Comp. and Math. with Appl., 57(2009)410-412.
S.Liang, D.J.Jeffrey, Comparison of homotopy analysis method and homotopy perturbation method through an evaluation equation, Commn nonlinear sci. numer. simulat., 14(2009)4057-4064.
D. N. Christodoulides, F. Lederer, and Y. Silberberg, Nature, 424, 817 (2003).
A. A. Sukhorukov, Y.S. Kivshar, H. S. Eisenberg, and Y. Silberberg, IEEE J. Quant. Electronics, 39, 31 (2003).
N. K. Efremidis et al., Phys. Rev. Lett., 91, 213906 (2003).
J. W. Fleischer, M. Segev, N. K. Efremidis, and D. N. Christodoulides, Nature, 422, 147 (2003).
M.J. Ablowitz, N. Antar, I. Bakrta , B. Ilan, Phys, Rev. A, 81, (2010) 033834.
J. Yang, Nonlinear Waves in Integrable and Nonintegrable Systems, Society for Industrial and Applied Mathematics, Philadelphia.