Approximate Symmetry Reduction to the Perturbed One-Dimensional Nonlinear Schrödinger Equation

doi:10.1088/0256-307X/26/2/020201

Chin. Phys. Lett.

2009, Vol. 26

Issue (2): 020201 DOI: 10.1088/0256-307X/26/2/020201

GENERAL

Approximate Symmetry Reduction to the Perturbed One-Dimensional Nonlinear Schrödinger Equation

JIA Man¹, WANG Jian-Yong², LOU Sen-Yue ^1,2,3

¹Department of Physics, Shanghai Jiao Tong University, Shanghai 200240²Science Faculty of Ningbo University, Ningbo 315211³School of Mathematical Science, Fudan University, Shanghai 200433

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JIA Man, WANG Jian-Yong, LOU Sen-Yue 2009 Chin. Phys. Lett. 26 020201

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Abstract The one-dimensional nonlinear Schrödinger equation with a perturbation of polynomial type is considered. Using the approximate symmetry perturbation theory, the approximate symmetries and approximate symmetry reduction equations are obtained.

Keywords: 02.03.Ik 02.30.Jr

Received: 19 September 2008 Published: 20 January 2009

PACS:	02.03.Ik
	02.30.Jr	(Partial differential equations)

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https://cpl.iphy.ac.cn/10.1088/0256-307X/26/2/020201 OR https://cpl.iphy.ac.cn/Y2009/V26/I2/020201

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[1] Ablowitz M, Clarkson P 1991 Solitons, NonlinearEvolution Equations and Inverse Scattering (Cambridge: CambridgeUniversity Press)
[2] Fushchich W I and Shtelen W M 1989 J. Phys. A: Math.Gen. 22 L887
[3] Abdullaev F Kh, Bronski J C and Papanicolaou G 2000 Physica D 135 369
[4] Euler N, Shulga M W and Steeb W H 1992 J. Phys. A:Math. Gen. 25 1095
[5] Euler M, Euler N and K\"oler A 1994 J. Phys. A: Math.Gen. 27 2083
[6] Euler N and Euler M 1994 Nonlinear Math. Phys. 1 41
[7] Fushchich W I and Shtelen W H 1989 J. Phys. A: Math.Gen. 22 887
[8] Jiao X Y, Yao R X and Lou S Y 2008 J. Math. Phys. 49 093505

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