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A Compact Scheme for Coupled Stochastic Nonlinear Schrödinger Equations

  • Chuchu Chen (a1), Jialin Hong (a1), Lihai Ji (a2) and Linghua Kong (a3)

In this paper, we propose a compact scheme to numerically study the coupled stochastic nonlinear Schrödinger equations. We prove that the compact scheme preserves the discrete stochastic multi-symplectic conservation law, discrete charge conservation law and discrete energy evolution law almost surely. Numerical experiments confirm well the theoretical analysis results. Furthermore, we present a detailed numerical investigation of the optical phenomena based on the compact scheme. By numerical experiments for various amplitudes of noise, we find that the noise accelerates the oscillation of the soliton and leads to the decay of the solution amplitudes with respect to time. In particular, if the noise is relatively strong, the soliton will be totally destroyed. Meanwhile, we observe that the phase shift is sensibly modified by the noise. Moreover, the numerical results present inelastic interaction which is different from the deterministic case.

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*Corresponding author. Email (C. Chen), (J. Hong), (L. Ji), (L. Kong)
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[1] P.G.Drazin , Solitons, in: London Mathematical Society Lecture Note Series, Cambridge University Press, Cambridge, 1983.

[2] A.Debussche and L.D.Menza , Numerical simulation of focusing stochastic nonlinear Schrödinger equations, Physica D, 162 (2002), 131154.

[3] J.N.Elgin , Stochastic perturbations of optical solitons, Opt. Lett., 18 (1993), 1012.

[4] J.P.Gordon , Interacion forces among solitons in optical fibers, Opt. Lett., 8 (1983), 596598.

[5] A.Hasegawa , Optical solitons in fibers, Springer Berlin Heidelberg, 1989.

[6] E.Hairer , C.Lubich and G.Wanner . Geometric numerical integration, New York: Springer-Verlag, 2006.

[8] Y.Kodama , M.Romagnoli and S.Wabnitz , Soliton stability and interactions in fibre lasers, Electron. Lett., 28 (1992), 19811983.

[9] L.Kong , J.Hong , L.Ji and P.Zhu , Compact and efficient conservative schemes for coupled nonlinear Schrödinger equations, Numer. Methods Partial Differential Eq., 31 (2015), 18141843.

[10] W.Liu , N.Pan , L.Huang and M.Lei , Soliton interactions for coupled nonlinear Schrödinger equations with symbolic computation, Nonlinear Dynam., 78 (2014), 755770.

[11] S.K.Lele , Compact finite difference schemes with spectral-like resolution, J. Comput. Phys., 103 (1992), 1642.

[12] F.M.Mitschke and L.F.Mollenauer , Experimental observation of interaction forces between solitons in optical fibers, Opt. Lett., 12 (1987), 355357.

[13] B.A.Malomed , Bound solitons in coupled nonlinear Schrödinger equations, Phys. Rev. A, 45 (1992), R8321.

[14] J.Sun , X.Gu and Z.Ma , Numerical study of the soliton waves of the coupled nonlinear Schrödinger system, Physica D, 196 (2004), 311328.

[15] Z.Sun , Y.Gao , X.Yu and Y.Liu , Switching of bound vector solitons for the coupled nonlinear Schrödinger equations with nonhomogenously stochastic perturbations, Chaos, 22 (2012), 043132.

[16] T.Ueda and W.L.Kath , Dynamics of optical pulses in randomly birefringent fibers, Physica D, 55 (1992), 166181.

[17] P.K.A.Wai , C.R.Menyuk and H.Chen , Stability of solitons in randomly varying birefringent fibers, Opt. Lett., 16 (1991), 12311233.

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Communications in Computational Physics
  • ISSN: 1815-2406
  • EISSN: 1991-7120
  • URL: /core/journals/communications-in-computational-physics
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