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NEW EXACT SOLUTIONS OF COUPLED (2+1)-DIMENSIONAL NONLINEAR SYSTEMS OF SCHRÖDINGER EQUATIONS

Part of: Equations of mathematical physics and other areas of application Partial differential equations, initial value and time-dependent initial-boundary value problems

Published online by Cambridge University Press:  03 May 2011

F. KHANI ,
M. T. DARVISHI ,
A. FARMANY  and
L. KAVITHA
F. KHANI
Affiliation:
Young Researchers Club, Islamic Azad University, Ilam Branch, Iran (email: farzad_khani59@yahoo.com)
M. T. DARVISHI
Affiliation:
Department of Mathematics, Razi University, Kermanshah, Iran (email: darvishimt@yahoo.com)
A. FARMANY*
Affiliation:
Islamic Azad University, Ilam Branch, Iran (email: a.farmany@usa.com)
L. KAVITHA
Affiliation:
Department of Physics, Periyar University, Salem-636 011, India (email: louiskavitha@yahoo.co.in)
*
✉For correspondence; e-mail: a.farmany@usa.com
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Abstract

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The Exp-function method is applied to construct a new type of solution of the coupled (2+1)-dimensional nonlinear system of Schrödinger equations. It is shown that the method provides a powerful mathematical tool for solving nonlinear evolution equations in mathematical physics.

Keywords

Schrödinger equationsExp-function methodexact solutionnonlinear evolution equations

MSC classification

Secondary: 65M99: None of the above, but in this section 35Q90: PDEs in connection with mathematical programming

Information

Type
Research Article
Information
The ANZIAM Journal , Volume 52 , Issue 1 , July 2010 , pp. 110 - 121
Copyright
Copyright © Australian Mathematical Society 2011

References

[1]Abdou, M. A., Soliman, A. A. and El-Basyony, S. T., “New application of Exp-function method for improved Boussinesq equation”, Phys. Lett. A 369 (2007) 469–475.CrossRefGoogle Scholar
[2]Ablowitz, M. J. and Segur, H., Solitons and the inverse scattering transform (SIAM, Philadelphia, 1981).CrossRefGoogle Scholar
[3]Bai, C. L. and Zhao, H., “Generalized extended tanh-function method and its application”, Chaos Solitons Fractals 27 (2006) 1026–1035.CrossRefGoogle Scholar
[4]Darvishi, M. T., “Preconditioning and domain decomposition schemes to solve PDEs”, Int. J. Pure Appl. Math. 1 (2004) 419–439.Google Scholar
[5]Darvishi, M. T. and Javidi, M., “A numerical solution of Burgers’ equation by pseudospectral method and Darvishi’s preconditioning”, Appl. Math. Comput. 173 (2006) 421–429.Google Scholar
[6]Darvishi, M. T., Karami, A. and Shin, B.-C., “Application of He’s parameter-expansion method for oscillators with smooth odd nonlinearities”, Phys. Lett. A 372 (2008) 5381–5384.CrossRefGoogle Scholar
[7]Darvishi, M. T. and Khani, F., “Application of He’s homotopy perturbation method to stiff systems of ordinary differential equations”, Z. Naturforschung (2008) 19–23.CrossRefGoogle Scholar
[8]Darvishi, M. T. and Khani, F., “Numerical and explicit solutions of the fifth-order Korteweg–de Vries equations”, Chaos Solitons Fractals 39 (2009) 2484–2490.CrossRefGoogle Scholar
[9]Darvishi, M. T., Khani, F. and Kheybari, S., “Spectral collocation solution of a generalized Hirota-Satsuma KdV equation”, Int. J. Comput. Math. 84 (2007) 541–551.CrossRefGoogle Scholar
[10]Darvishi, M. T., Khani, F. and Kheybari, S., “Spectral collocation method and Darvishi’s preconditionings to solve the generalized Burgers–Huxley equation”, Commun. Nonlinear Sci. Numer. Simul. 13 (2008) 2091–2103.CrossRefGoogle Scholar
[11]Darvishi, M. T., Khani, F. and Soliman, A. A., “The numerical simulation for stiff systems of ordinary differential equations”, Comput. Math. Appl. 54 (2007) 1055–1063.CrossRefGoogle Scholar
[12]Darvishi, M. T., Kheybari, S. and Khani, F., “A numerical solution of the Korteweg–de Vries equation by pseudospectral method using Darvishi’s preconditionings”, Appl. Math. Comput. 182 (2006) 98–105.Google Scholar
[13]Davey, A. and Stewartson, K., “On three-dimensional packets of surface waves”, Proc. R. Soc. Lond. Ser. A 338 (1974) 101–110.Google Scholar
[14]Ebaid, A., “Exact solitary wave solutions for some nonlinear evolution equations via Exp-function method”, Phys. Lett. A 365 (2007) 213–219.CrossRefGoogle Scholar
[15]He, J. H., “Variational iteration method—a kind of non-linear analytical technique: some examples”, Int. J. Nonlinear Mech. 34 (1999) 699–708.CrossRefGoogle Scholar
[16]He, J. H., “Bookkeeping parameter in perturbation methods”, Int. J. Nonlinear Sci. Numer. Simul. 2 (2001) 257.CrossRefGoogle Scholar
[17]He, J. H., “New interpretation of homotopy perturbation method”, Internat. J. Modern Phys. B 20 (2006) 2561–2568.CrossRefGoogle Scholar
[18]He, J. H. and Wu, X. H., “Exp-function method for nonlinear wave equations”, Chaos Solitons Fractals 30 (2006) 700–708.CrossRefGoogle Scholar
[19]Khani, F., “Analytic study on the higher order Ito equations: new solitary wave solutions using the Exp-function method”, Chaos Solitons Fractals 41 (2009) 2128–2134.CrossRefGoogle Scholar
[20]Khani, F., Hamedi-Nezhad, S., Darvishi, M. T. and Ryu, S. W., “New solitary wave and periodic solutions of the foam drainage equation using the Exp-function method”, Nonlinear Anal. Real World Appl. 10 (2009) 1904–1911.CrossRefGoogle Scholar
[21]Khani, F., Hamedi-Nezhad, S. and Molabahrami, A., “A reliable treatment for nonlinear Schrödinger equations”, Phys. Lett. A 371 (2007) 234–240.CrossRefGoogle Scholar
[22]Khani, F., Samadi, F. and Hamedi-Nezhad, S., “New exact solutions of the Brusselator Reaction Diffusion model using the Exp-Function method”, Math. Probl. Eng. 2009. Article ID 346461, doi:10.1155/2009/346461.CrossRefGoogle Scholar
[23]Molabahrami, A., Khani, F. and Hamedi-Nezhad, S., “Soliton solutions of the two-dimensional KdV–Burgers equation by homotopy perturbation method”, Phys. Lett. A 370 (2007) 433–436.CrossRefGoogle Scholar
[24]Nishinari, K., Abe, K. and Satsuma, J., “A new type of soliton behavior in a two dimensional plasma system”, J. Phys. Soc. Japan 62 (1993) 2021–2029.CrossRefGoogle Scholar
[25]Pedit, F. and Hongyou, W., “Discretizing constant curvature surfaces via loop group factorizations: the discrete sine- and sinh-Gordon equations”, J. Geom. Phys. 17 (1995) 245–260.CrossRefGoogle Scholar
[26]Shin, B.-C., Darvishi, M. T. and Barati, A., “Some exact and new solutions of the Nizhnik–Novikov–Vesselov equation using the Exp-function method”, Comput. Math. Appl. 58 (2009) 2147–2151.CrossRefGoogle Scholar
[27]Shin, B.-C., Darvishi, M. T. and Karami, A., “Application of He’s parameter-expansion method to a nonlinear self-excited oscillator system”, Int. J. Nonlinear Sci. Num. Simul. 10 (2009) 137–1433.CrossRefGoogle Scholar
[28]Wazwaz, A. M., “The tanh method: solitons and periodic solutions for the Dodd–Bullough–Mikhailov and the Tzitzeica–Dodd–Bullough equations”, Chaos Solitons Fractals 25 (2005) 55–63.CrossRefGoogle Scholar
[29]Wu, X. H. and He, J. H., “Solitary solutions, periodic solutions and compacton-like solutions using the Exp-function method”, Comput. Math. Appl. 54 (2007) 966–986.CrossRefGoogle Scholar
[30]Yomba, E., “The modified extended Fan’s sub-equation method and its application to (2+1)-dimensional dispersive long wave equation”, Chaos Solitons Fractals 26 (2005) 785–794.CrossRefGoogle Scholar
[31]Zhang, J. F., “Homogeneous balance method and chaotic and fractal solutions for the Nizhnik–Novikov–Veselov equation”, Phys. Lett. A 313 (2003) 401–407.CrossRefGoogle Scholar
[32]Zhang, S., “New exact solutions of the KdV–Burgers–Kuramoto equation”, Phys. Lett. A 358 (2006) 414–420.CrossRefGoogle Scholar
[33]Zhang, S., “Application of Exp-function method to a KdV equation with variable coefficients”, Phys. Lett. A 365 (2007) 448–453.CrossRefGoogle Scholar
[34]Zhao, X., Wang, L. and Sun, W., “The repeated homogeneous balance method and its applications to nonlinear partial differential equations”, Chaos Solitons Fractals 28 (2006) 448–453.CrossRefGoogle Scholar