Multisymplectic Structure of a Finite Difference Scheme for a Complex Nonlinear System

Ram Dayal Pankaj; Arun Kumar

doi:https://doi.org/10.14445/22315373/IJMTT-V52P577

International Journal of Mathematics Trends and Technology

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Volume 52 | Number 8 | Year 2017 | Article Id. IJMTT-V52P577 | DOI : https://doi.org/10.14445/22315373/IJMTT-V52P577

Multisymplectic Structure of a Finite Difference Scheme for a Complex Nonlinear System

Ram Dayal Pankaj, Arun Kumar

Abstract

A Numerical study for the complex nonlinear system (coupled 1D nonlinear Schrödinger system (CNLS)) is considered as a Model for Complex Nonlinear System which is also a model for wave-wave interaction in ionic media. A finite difference scheme is derived for the model equations. A new six point scheme, which is equivalent to the multi-symplectic integrator, is derived. We investigate the conservation property of the multi-symplectic integrator of the complex nonlinear system (CNLS). The numerical simulation is also presented for the model equations.

Keywords

Coupled 1D nonlinear Schrödinger system; Multi-symplectic scheme; Energy conservation; Six-point scheme.

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Citation :

Ram Dayal Pankaj, Arun Kumar, "Multisymplectic Structure of a Finite Difference Scheme for a Complex Nonlinear System," International Journal of Mathematics Trends and Technology (IJMTT), vol. 52, no. 8, pp. 552-557, 2017. Crossref, https://doi.org/10.14445/22315373/IJMTT-V52P577