Binary Bargmann symmetry constraint associated with 3×3 discrete matrix spectral problem

Li, Xinyue; Zhao, Qiulan; Li, Yuxia; Dong, Huanhe

doi:10.22436/jnsa.008.05.05

Cited by 55 publications

(24 citation statements)

References 33 publications

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“…It has been an important work to study nonlinear PDE [1] due to their rich mathematical structures and features [2][3][4][5] as well as important applications in fluid dynamics and plasma physics [6][7][8][9][10][11][12]. Although many theories and methods were proposed to discuss the PDE [13][14][15][16][17][18][19][20], however, most nonlinear PDE have no analytic solutions; numerical methods are necessary to study hydrodynamic characteristics of PDEs [21][22][23][24].…”

Section: Formulation Of the Problem Of Interest For This Investigationmentioning

confidence: 99%

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The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Dong

Yang

2018

Mathematics

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We develop a Lax–Wendroff scheme on time discretization procedure for finite volume weighted essentially non-oscillatory schemes, which is used to simulate hyperbolic conservation law. We put more focus on the implementation of one-dimensional and two-dimensional nonlinear systems of Euler functions. The scheme can keep avoiding the local characteristic decompositions for higher derivative terms in Taylor expansion, even omit partly procedure of the nonlinear weights. Extensive simulations are performed, which show that the fifth order finite volume WENO (Weighted Essentially Non-oscillatory) schemes based on Lax–Wendroff-type time discretization provide a higher accuracy order, non-oscillatory properties and more cost efficiency than WENO scheme based on Runge–Kutta time discretization for certain problems. Those conclusions almost agree with that of finite difference WENO schemes based on Lax–Wendroff time discretization for Euler system, while finite volume scheme has more flexible mesh structure, especially for unstructured meshes.

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Section: Formulation Of the Problem Of Interest For This Investigationmentioning

confidence: 99%

“…The sliding average is U(x, y, t + ∆t) = U(x, y, t) + ∆tU (x, y, t) + (∆t 2 ) 2 U (x, y, t) + (∆t) 3 6 U (x, y, t) + (∆t) 4 24 U (4) (x, y, t) + ...,…”

Section: The Lax-wendroff-type Time Discretization Procedures For Eulementioning

confidence: 99%

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Dong

Yang

2018

Mathematics

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“…Many efficient techniques, such as homogeneous balance technique [47], symmetry theory [48], Jacobi elliptic function method [49], homotopy analysis transform method [50], homotopy perturbation transform method [51], Darboux transformation [52][53][54], Bilinear method [55,56], and so on [57], have been proposed to seek solitary waves solutions. In addition, some numerical methods, i.e., modified binomial and Monte Carlo methods [58], high accurate NRK, and MWENO [59][60][61], have also been used to solve partial differential equations.…”

Section: Introductionmentioning

confidence: 99%

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

et al. 2018

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In the present paper, a new partial differential equation has been obtained to describe the Rossby solitary waves with complete Coriolis force by employing multi-scale analysis and perturbation method, we call it combined ZK-mZK equation. The equation can reflect the propagation of Rossby waves on the plane and is more appropriate for the real ocean and atmosphere than the (1 + 1) dimensional models (such as KdV and mKdV), which can only represent the propagation of Rossby solitary waves in a line. Furthermore, by adopting the multiplier method, we construct conservation laws of the combined ZK-mZK equation, which is meaningful for researching the global stability of solutions. Finally, we deduce the exact solutions of the combined ZK-mZK equation via the semi-inverse variational principle. By applying these exact solutions, some propagation features of Rossby solitary waves are analyzed.

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“…As we all know, the generation of integrable system, determination of exact solution, and the properties of the conservation laws are becoming more and more rich [1][2][3][4][5]; in particular, the discrete integrable systems have many applications in statistical physics, quantum physics, and mathematical physics [6][7][8][9][10][11]. It is worth discussing the properties of discrete integrable systems, such as Darboux transformations [12,13], Hamiltonian structures [14][15][16], exact solutions [17], and the transformed rational function method [18].…”

Section: Introductionmentioning

confidence: 99%

Algebro-Geometric Solutions for a Discrete Integrable Equation

Tao

Dong

2017

Discrete Dynamics in Nature and Society

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With the assistance of a Lie algebra whose element is a matrix, we introduce a discrete spectral problem. By means of discrete zero curvature equation, we obtain a discrete integrable hierarchy. According to decomposition of the discrete systems, the new differential-difference integrable systems with two-potential functions are derived. By constructing the Abel-Jacobi coordinates to straighten the continuous and discrete flows, the Riemann theta functions are proposed. Based on the Riemann theta functions, the algebro-geometric solutions for the discrete integrable systems are obtained.

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Binary Bargmann symmetry constraint associated with 3×3 discrete matrix spectral problem

Cited by 55 publications

References 33 publications

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

The Finite Volume WENO with Lax–Wendroff Scheme for Nonlinear System of Euler Equations

Combined ZK-mZK equation for Rossby solitary waves with complete Coriolis force and its conservation laws as well as exact solutions

Algebro-Geometric Solutions for a Discrete Integrable Equation

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