Generalized fractional supertrace identity for Hamiltonian structure of NLS–MKdV hierarchy with self-consistent sources

Dong, Huan He; Guo, Baoyong; Yin, Bin

doi:10.1007/s13324-015-0115-3

Cited by 64 publications

(26 citation statements)

References 16 publications

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“…There are several commonly used definitions of fractional order derivative [9,[11][12][13][14][15][16]. We utilize Caputo fractional order derivative in this paper.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

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A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Lu¹,

Wang²,

Dan³

2017

Mathematical Problems in Engineering

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Considering the popular use of a certain kind of supervision management problem in many fields, we firstly build an ordinary supervision game model of multiple stakeholders. Secondly, a fractional supervision game model is set up and solved based on the theory of fractional calculus and a predictor-corrector numerical approach. Thirdly, the methods of phase diagram and time series graph were applied to simulate and analyse the dynamic process of the fractional order game model. Results of numerical solutions are given to illustrate our conclusions and referred to the practice.

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“…There are several commonly used definitions of fractional order derivative [9,[11][12][13][14][15][16]. We utilize Caputo fractional order derivative in this paper.…”

Section: Fractional Order Calculusmentioning

confidence: 99%

“…According to the model assumptions made in Section 2, the parameters of the game model (15) and initial values of variables are supposed as…”

Section: Numerical Simulation Of the Fractional Game Modelmentioning

confidence: 99%

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Lu¹,

Wang²,

Dan³

2017

Mathematical Problems in Engineering

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“…In [2], by means of a fixed point theorem, Bai is the Riemann-Liouville fractional derivative, f is a Carathédory function, and f (t, x, y, z) is singular at the value 0 of its arguments x, y, z. Some recent contributions of fractional differential equations can be seen in [1][2][3][4][5][6][7][8][10][11][12][13][14][15][16][17][18][19][20][21][22][23].…”

Section: Introductionmentioning

confidence: 99%

Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition

Song

Bai

2018

Adv Differ Equ

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“…The problem of propagation of nonlinear wave in plasma and fluid can be described by differential equations such as the KDV equation, the mKDV equation, the NLS equation, and the Boussinesq equation [12][13][14][15][16][17][18][19][20]. The NLS equation describes the time-space evolution of slow-changing envelopes, it has high theoretical value in quantum matters and has been extensively used in various branches of physics, such as optics, envelope gravity waves etc.…”

Section: Introductionmentioning

confidence: 99%

Time–space fractional ( 2 + 1 ) $(2+1)$ dimensional nonlinear Schrödinger equation for envelope gravity waves in baroclinic atmosphere and conservation laws as well as exact solutions

Yang

2018

Adv Differ Equ

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In this article, nonlinear propagation of envelope gravity waves is studied in baroclinic atmosphere. The classical (2 + 1) dimensional nonlinear Schrödinger (NLS) equation can be derived by using the multiple-scale, perturbation method. Further, via the semi-inverse method, the Euler-Lagrange equation and Agrawal's method, the time-space fractional (2 + 1) dimensional nonlinear Schrödinger (FNLS) equation is obtained to describe the envelope gravity waves. Furthermore, the conservation laws of time-space FNLS equation are discussed on the basis of Lie group analysis method. Finally, the exact solutions to the equation are given by employing the exp(-φ(ξ )) method. The results demonstrate that the nonlinear effect caused by the fractional order leads to the change of the propagation characteristics of envelope gravity waves, the construction of fractional model has far-reaching significance for the research of nonlinear propagation of envelope gravity waves in actual atmospheric and ocean movement.

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Generalized fractional supertrace identity for Hamiltonian structure of NLS–MKdV hierarchy with self-consistent sources

Cited by 64 publications

References 16 publications

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

A Fractional Supervision Game Model of Multiple Stakeholders and Numerical Simulation

Positive solutions of fractional differential equations involving the Riemann–Stieltjes integral boundary condition

Time–space fractional ( 2 + 1 ) $(2+1)$ dimensional nonlinear Schrödinger equation for envelope gravity waves in baroclinic atmosphere and conservation laws as well as exact solutions

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