Total views : 135

New Solutions for Nonlinear Schrodinger Equations using Adomian Decomposition and Homotopy Perturbation Methods

Affiliations

  • Centre of Foundation Studies for Agriculture Science, Universiti Putra Malaysia, 43400 UPM Serdang, Selangor,, Malaysia

Abstract


Coupled non-linear Schrodinger equation (CNLS) with two mode propagations in an optical fibre was studied. Using Painleve analysis, we are successfully solving the focusing Manakov system, bright and dark solitons using Adomian Decomposition Method (ADM) and Homotopy Perturbation Method (HPM). Both methods are fast convergent, do not need linearization and eliminates massive computation work. Its hows that HPM does not involve the Adomian polynomials when dealing with non-linear problems.

Keywords

Adomian Decomposition, Homotopy Pertubation, Schrodinger, Soliton.

Full Text:

 |  (PDF views: 109)

References


  • Mollenauer LF, Gordon JP. Solitons in Optical Fibers: fundamentals and applications. Academic Press; 2006 Mar 8.
  • Agrawal GP. Nonlinear Fiber Optics. Academic Press; 1977.
  • Curtis R. Nonlinear pulse propagation in birefringertoptical fibers, IEEE Journal of Quantum electronics. 1987 Feb; 23(2):175.
  • Garth SJ, Park C. Nonlinear effects in elliptical-core few mode optical fibre. JOSA B. 1992 Feb 1; 9(2): 243–50.
  • Radhakrishnan R, Lakshmanan M. Bright and dark soliton solutions to coupled nonlinear Schrodinger equations.Journal of Physics A: Mathematical and General. 1995 May 7; 28(9): 2683.
  • Reichel B, Leble S. On convergence and stability of anumerical scheme of coupled Nonlinear Schrodinger Equations.Computer and Mathemathics with Applications. 2008 Feb 29; 55(4): 745–59.
  • Denes P, Finley JD. Bäcklund transformations for general PDE’s. Physica D: Nonlinear Phenomena.1983 Oct 31; 9(1): 236–50.
  • Hu XB, Wu YT. Application of the Hirotabilinear formalism to anewintegrable differential-difference equation.Physics Letters A. 1998 Sep 28; 246(6): 523–9.
  • Coley AA, editor. Bäcklundand Darboux Transformations: the geometry of solutions: AARMS-CRM Workshop, 1999 Jun 4–9, Halifax, NS, Canada. American Mathematical Soc.; 2001.
  • Fan E. Extendedtanh-function method and its applications to nonlinear equations. Physics Letters A. 2000 Dec 4; 277(4): 212–8.
  • Yusufoglu E. Homotopy perturbation method for solving a nonlinear system of second order boundary value problems.International Journal of Nonlinear Sciences and Numerical Simulation. 2007; 8(3): 353–8.
  • Wazwaz AM. Asine-cosine method for handling nonlinear wave equations. Mathematical and Computer modelling.2004 Sep 30; 40(5): 499–508.
  • He JH. Variationaliteration method-a kind of non-linear analytical technique: some examples. Internationaliteration method-a kind of non-linear mechanic. 1999 Jul 31; 34(4): 699–708.
  • Adomian G. A review of the decomposition method and some recent results for nonlinear equations. Computers & Mathematics with Applications. 1991 Dec 31; 21(5): 101– 27.
  • He JH. Homotopy perturbation technique. Computer methods in applied mechanics and engineering. 1999 Aug 31; 178(3): 257–62.
  • Mahiddin N, Hashim Ali SA. Approximate Analytical Solutions for Mathematical Model of Tumour Invasion and Metastasis Using Modified Adomian Decomposition and Homotopy Perturbation Methods. Journal of Applied Mathematics. 2014 Jan 30; 2014.
  • Sahadevan R, Tamizhmani KM, Lakshmanan M. Painleve analysis and integrability of coupled non-linear Schrodinger equations. Journal of Physics A: Mathematical and General.1986 Jul 11; 19(10): 1783.
  • Manakov SV. On the theory of two-dimensional stationary self-focusing of electromagnetic waves. Soviet PhysicsJETP. 1974 Feb; 38(2): 248–53.

Refbacks

  • There are currently no refbacks.


Creative Commons License
This work is licensed under a Creative Commons Attribution 3.0 License.