Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method
Zhang Rong-Pei(张荣培)a)†, Yu Xi-Jun(蔚喜军)b), and Feng Tao (冯涛)b)
a. School of Sciences, Liaoning Shihua University, Fushun 113001, China; b. Laboratory of Computational Physics, Institute of Applied Physics and Computational Mathematics, Beijing 100088, China
Abstract In this work, we present the direct discontinuous Galerkin (DDG) method for the one-dimensional coupled nonlinear Schr?dinger (CNLS) equation. We prove that the new discontinuous Galerkin method preserves the discrete mass conservations corresponding to the properties of the CNLS system. The ordinary differential equations obtained by the DDG space discretization is solved via a third-order stabilized Runge-Kutta method. Numerical experiments show that the new DDG scheme gives stable and less diffusive results and has excellent long-time numerical behaviors for the CNLS equations.
Zhang Rong-Pei(张荣培), Yu Xi-Jun(蔚喜军), and Feng Tao (冯涛) Solving coupled nonlinear Schrödinger equations via a direct discontinuous Galerkin method 2012 Chin. Phys. B 21 030202
[1]
Dhar A K and Das K P 1991 Phys. Fluids 3 3021
[2]
Menyuk C R 1988 J. Opt. Soc. Am. B Opt. Phys. 5 392
[3]
Radhakrishnan R, Lakshmanan M and Hietarinta J 1997 Phys. Rev. E 56 2213
[4]
Liu G T 2006 Chin. Phys. 16 2500
[5]
Li B Q, Ma Y L, Wang C, Xu M P and Li Y 2011 Acta Phys. Sin. 60 060203 (in Chinese)
[6]
Ismail M S and Taha T R 2001 Math. Comput. Simul. 56 547
[7]
Wang T C, Guo B L and Zhang L M 2010 Appl. Math. Comput. 217 1604
[8]
Wang H 2005 Appl. Math. Comput. 170 17
[9]
Ismail M S 2008 Math. Comput. Simul. 78 532
[10]
Cheng X P, Ji L and Ye L J 2007 Chin. Phys. 16 2503
[11]
Mokhtari R, Samadi T A and Chegini N G 2011 Chin. Phys. Lett. 28 020202
[12]
Utsumi T, Aoki T, Koga J and Yamagiwa M 2006 Commun. Comput. Phys. 1 261
[13]
Sun J Q and Qin M Z 2003 Comput. Phys. Commun. 155 221
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