Full Information H2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

Ma, Haiying; Wang, Yang

doi:10.3390/math10010037

Cited by 19 publications

(4 citation statements)

References 28 publications

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“…Nonlinear problems are always full of infinite charm and challenges. Some meaningful developments of nonlinear models deserve attention, such as the H 2 optimal controller of coupled stochastic algebraic Riccati equations [32], and the influence of higher-order nonlinear effects on optical solitons [33].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

Zhang¹,

Liu²

2022

Commun. Theor. Phys.

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The purpose of this paper is to report the feasibility of constructing high-order rogue waves with controllable fission and asymmetry for high-dimensional nonlinear evolution equations. Such a nonlinear model considered in this paper as the concrete example is the (3+1)-dimensional generalized Boussinesq (gB) equation, and the corresponding method is Zhaqilao’s symbolic computation approach containing two embedded parameters. It is indicated by the (3+1)-dimensional gB equation that the embedded parameters can not only control the center of the first-order rogue wave, but also control the number of the wave peaks split from higher-order rogue waves and the asymmetry of higher-order rogue waves about the coordinate axes. The main novelty of this paper is that the obtained results and findings can provide useful supplements to the method used and the controllability of higher-order rogue waves.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

Zhang¹,

Liu²

2022

Commun. Theor. Phys.

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“…An iterative method for solving for approximate solutions of (41) maybe found in [16]. Keeping in mind the boundary condition (2) at t = 1, we calculate I 1−α 0 + y(t, λ) and then evaluate this at t = 1 in order to find the dispersion relation for the eigenvalues.…”

Section: Existence and Asymptotic Distribution Of The Eigenvaluesmentioning

confidence: 99%

Fractional Sturm–Liouville Eigenvalue Problems, II

Dehghan

Mingarelli

2022

Fractal Fract

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We continue the study of a non-self-adjoint fractional three-term Sturm–Liouville boundary value problem (with a potential term) formed by the composition of a left Caputo and left Riemann–Liouville fractional integral under Dirichlet type boundary conditions. We study the existence and asymptotic behavior of the real eigenvalues and show that for certain values of the fractional differentiation parameter α, 0<α<1, there is a finite set of real eigenvalues and that, for α near 1/2, there may be none at all. As α→1− we show that their number becomes infinite and that the problem then approaches a standard Dirichlet Sturm–Liouville problem with the composition of the operators becoming the operator of second order differentiation.

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“…To date, many fundamental properties of the equation have been studied from the equation itself, including the Hamiltonian structure, 26 and Borel-measurable Markov jump systems. 27 A great deal of work has been carried out by many mathematicians and physicists on nonlinear equations, and they have found a variety of complex solution methods, such as sine-cosine method, 28 ( G ′ / G ) -expansion method, 29 Darboux transformation method, 30 Jacobi elliptic function expansion method, 31,32 Bäcklund transformation method, 33,34 and so on.…”

Section: Introductionmentioning

confidence: 99%

Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

Zhao

Wang

2023

Advances in Mechanical Engineering

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A forced KdV equation including the special topography effect is derived to describe nonlinear long wave and solitary eddy based on the quasi-geostrophic potential vorticity model. We obtain the theoretical solution of the equation and the concrete form of stream function through perturbation theory and multi-scale analysis methods. It is found that the joint effect of weak shear basic flow and topography can change the cyclone and anticyclone structure of eddy, and in the meantime topographic structure affects the East-West propagation direction of solitary wave. Finally, according to the interaction between nonlinear long wave and topography by pseudo spectral numerical method, the topographic height is related to the amplitude, wavelength and wave velocity of the excited wave train, and the topography affects not only the spatial structure of wave, but also the amplitude of wave.

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Full Information H2 Control of Borel-Measurable Markov Jump Systems with Multiplicative Noises

Cited by 19 publications

References 28 publications

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

Higher-order rogue waves with controllable fission and asymmetry localized in a (3 + 1)-dimensional generalized Boussinesq equation

Fractional Sturm–Liouville Eigenvalue Problems, II

Forced solitary wave and vorticity with topography effect in quasi-geostrophic modelling

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