2015
DOI: 10.1016/j.apm.2015.01.068
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Abstract: In this article, we discuss the conservation laws for the nonlinear Schrödinger equation with wave operator under multi-symplectic integrator (MI). First, the conservation laws of the continuous equation are presented and one of them is new. The multisymplectic structure and MI are constructed for the equation. The discrete conservation laws of the numerical method are analyzed. It is verified that the proposed MI can stably simulate the Hamiltonian PDEs excellently over long-term. It is more accurate than som… Show more

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Cited by 15 publications
(9 citation statements)
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“…Several numerical algorithms have been studied for solving the NSEW (Refs. [3][4][5][6][7][8][9][10][11] and references therein). Recently, structure-preserving algorithms were proposed to solving the Hamiltonian systems [12][13][14][15] and applied to various PDEs, such as the nonlinear Schrödingertype equation [16][17][18][19], wave equation [20], and KdV equation [21].…”
Section: Introductionmentioning
confidence: 99%
“…Several numerical algorithms have been studied for solving the NSEW (Refs. [3][4][5][6][7][8][9][10][11] and references therein). Recently, structure-preserving algorithms were proposed to solving the Hamiltonian systems [12][13][14][15] and applied to various PDEs, such as the nonlinear Schrödingertype equation [16][17][18][19], wave equation [20], and KdV equation [21].…”
Section: Introductionmentioning
confidence: 99%
“…There are many findings about the single nonlinear Schrödinger (NLS) equation and two‐component coupled nonlinear Schrödinger equations both from purely mathematics and numerical solvers due to their interesting features and wide application. () For the single NLS equation, Bao et al proposed a time‐splitting scheme for 2D NLS equation with a dimensionless parameter and vortex on a bounded domain . Fu et al proposed an improved alternative direction implicit scheme for multidimensional Schrödinger equation .…”
Section: Introductionmentioning
confidence: 99%
“…Equations of this type have many different applications in Physics, such as nonrelativistic limit of the Klein-Gordon equation [25,26,28], Langmuir wave envelope approximation in plasma physics [4], model of planar light bullets [2,34] and so forth. For this reason, it has been subject of investigation, both from a theoretical (see, e.g., [21]) and, more recently, also from a numerical point of view (see, e.g., [1,19,20,23,24,[29][30][31][32][33]). We here consider the case where the equation (1.1) is completed with the initial conditions: Consequently, both u 0 and v 0 will be assumed to be periodic functions, regular enough (as a periodic function).…”
Section: Introductionmentioning
confidence: 99%