Weak multi-symplectic reformulation and geometric numerical integration for the nonlinear Schrödinger equations with delta potentials

Bai, Jiejing; Li, Chun; Liu, Xiaoyan

doi:10.1093/imanum/drw062

Cited by 4 publications

(2 citation statements)

References 17 publications

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“…Using the method of line, we first consider how to discretize properly the derivative of the flux, i.e. ¶ f x (see equation (10)). The key is to use a so-called staggered grid.…”

Section: Numerical Schemementioning

confidence: 99%

“…Viewing the problem as an interface at the point x=0, a so-called explicit jump immersed interface method is proposed in [9]. A weak multi-symplectic reformulation is proposed in [10,11] for equation (1), enabling one to get some preserving properties. One can also regularize the Dirac delta function in equation (1) by using a nonsingular function [12], resulting in an equation that can be handled by some common schemes.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Cheng

Chen

et al. 2020

Commun. Theor. Phys.

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“…Using the method of line, we first consider how to discretize properly the derivative of the flux, i.e. ¶ f x (see equation (10)). The key is to use a so-called staggered grid.…”

Section: Numerical Schemementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Cheng

Chen

et al. 2020

Commun. Theor. Phys.

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Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential

Zhou,

Cai,

Tang

et al. 2023

Calcolo

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Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation

Zhang,

Hu,

Wang

et al. 2023

J Nonlinear Math Phys

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Seeking solitary wave solutions and revealing their interactional characteristics for nonlinear evolution equations help us lot to comprehend the motion laws of the microparticles. As a local nonlinear dynamic behavior, the soliton-collision is difficult to be reproduced numerically. In this paper, the soliton-collision process in the nonlinear perturbed Schrödinger equation is simulated employing the multi-symplectic method. The multi-symplectic formulations are derived including the multi-symplectic form and three local conservation laws of the nonlinear perturbed Schrödinger equation. Employing the implicit midpoint rule, we construct a multi-symplectic scheme, which is equivalent to the Preissmann box scheme, for the nonlinear perturbed Schrödinger equation. The elegant structure-preserving properties of the multi-symplectic scheme are illustrated by the tiny maximum absolute residual of the discrete multi-symplectic structure at each time step in the numerical simulations. The effects of the perturbation strength on the soliton-collision in the nonlinear perturbed Schrödinger equation are reported in the numerical results in detail.

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Weak multi-symplectic reformulation and geometric numerical integration for the nonlinear Schrödinger equations with delta potentials

Cited by 4 publications

References 17 publications

Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Nonlinear Schrödinger equation with a Dirac delta potential: finite difference method

Accurate and efficient numerical methods for the nonlinear Schrödinger equation with Dirac delta potential

Multi-Symplectic Simulation on Soliton-Collision for Nonlinear Perturbed Schrödinger Equation

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