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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 |
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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.
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Received: 16 June 2011
Revised: 22 September 2011
Accepted manuscript online:
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PACS:
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02.30.Jr
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(Partial differential equations)
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02.70.Dh
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(Finite-element and Galerkin methods)
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| Fund: Project supported by the National Natural Science Foundation of China (Grant No 11171038). |
Corresponding Authors:
Zhang Rong-Pei,rongpeizhang@163.com
E-mail: rongpeizhang@163.com
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Cite this article:
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
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| [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
|
| [14] |
Sun J Q, Gu X Y and Ma Z Q 2004 Physica D 196 311
|
| [15] |
Cai J X 2010 Appl. Math. Comput. 216 2417
|
| [16] |
Yu Y and Shu C 2005 J. Comput. Phys. 205 72
|
| [17] |
Liu H and Yan J 2009 SIAM J. Numer. Anal. 47 675
|
| [18] |
Liu H and Yan J 2010 Commun. Comput. Phys. 8 541
|
| [19] |
Shu C W and Osher S 1988 J. Comput. Phys. 77 439
|
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