Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows

Liu, Yu; Dong, Huanhe; Zhang, Yong

doi:10.1007/s13324-018-0209-9

Cited by 19 publications

(18 citation statements)

References 25 publications

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“…Meanwhile, compared with the extensive study of various exact solutions for nonlinear evolution equation, such as soliton solutions and so on, for both discrete and continuous cases, [24][25][26][27][28] the study of interaction solutions has aroused great interest of researchers. [29][30][31][32][33][34] When lump solutions of Eq.…”

Section: Discussionmentioning

confidence: 99%

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Wang

et al. 2018

Mod. Phys. Lett. B

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Through symbolic computation with Maple, two classes of lump solutions, rationally localized in all directions in space, are presented for a new extended (2[Formula: see text]+[Formula: see text]1)-dimensional Boussinesq equation. Analyticity of the solutions is naturally achieved, and particularly, taking special choices of the involved parameters will guarantee the positiveness of the constant term in the quadratic function f. Moreover, it deserves a note that one parameter in f plays an important role in order to maintain the positiveness of the quadratic function f. As illustrative examples, two particular lump solutions with specific values of the involved parameters are worked out and their three-dimensional plots, contour plots, x-curves and y-curves are made.

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Section: Discussionmentioning

confidence: 99%

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Wang

et al. 2018

Mod. Phys. Lett. B

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“…The solution of the model is a relatively broad research area in science [50,51]. In this section, using the simplified Hirota bilinear method [24,52], we seek multiple soliton solutions of the 3D TSF-Schamel-KdV equation.…”

Section: Multi-soliton Solutions For the 3d Tsfschamel-kdv Equationmentioning

confidence: 99%

Study of Ion‐Acoustic Solitary Waves in a Magnetized Plasma Using the Three‐Dimensional Time‐Space Fractional Schamel‐KdV Equation

Guo

Zhang

et al. 2018

Complexity

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The study of ion-acoustic solitary waves in a magnetized plasma has long been considered to be an important research subject and plays an increasingly important role in scientific research. Previous studies have focused on the integer-order models of ionacoustic solitary waves. With the development of theory and advancement of scientific research, fractional calculus has begun to be considered as a method for the study of physical systems. The study of fractional calculus has opened a new window for understanding the features of ion-acoustic solitary waves and can be a potentially valuable approach for investigations of magnetized plasma. In this paper, based on the basic system of equations for ion-acoustic solitary waves and using multi-scale analysis and the perturbation method, we have obtained a new model called the three-dimensional(3D) Schamel-KdV equation. Then, the integerorder 3D Schamel-KdV equation is transformed into the time-space fractional Schamel-KdV (TSF-Schamel-KdV) equation by using the semi-inverse method and the fractional variational principle. To study the properties of ion-acoustic solitary waves, we discuss the conservation laws of the new time-space fractional equation by applying Lie symmetry analysis and the RiemannLiouville fractional derivative. Furthermore, the multi-soliton solutions of the 3D TSF-Schamel-KdV equation are derived using the Hirota bilinear method. Finally, with the help of the multi-soliton solutions, we explore the characteristics of motion of ionacoustic solitary waves.

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“…Authors were committed to finding ways to control infectious diseases from pathology, epidemiology, culture and other aspects. The mathematical modeling method is considered as an effective method to understand the development and evolution of variables [1][2][3][4][5][6][7][8][9][10][11][12][13]. Mathematical models have been used to study the spread and evolution of infectious diseases in the human population.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of a stochastic SIS epidemic model with nonlinear incidence rates

et al. 2019

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In this paper, considering the impact of stochastic environment noise on infection rate, a stochastic SIS epidemic model with nonlinear incidence rate is proposed and analyzed. Firstly, for the corresponding deterministic system, the threshold which determines the extinction or permanence of the disease is obtained by analyzing the stability of the equilibria. Then, for the stochastic system, the global dynamics is investigated by using the theory of stochastic differential equations; especially the threshold dynamics is explored when the stochastic environment noise is small. The results show that the condition for the epidemic disease to go to extinction in the stochastic system is weaker than that of the deterministic system, which implies that stochastic noise has a significant impact on the spread of infectious diseases and the larger stochastic noise is conducive to controlling the epidemic diseases. To illustrate this phenomenon, we give some computer simulations with different intensities of the stochastic noise.

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Solutions of a discrete integrable hierarchy by straightening out of its continuous and discrete constrained flows

Cited by 19 publications

References 25 publications

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Lump solutions of a new extended (2+1)-dimensional Boussinesq equation

Study of Ion‐Acoustic Solitary Waves in a Magnetized Plasma Using the Three‐Dimensional Time‐Space Fractional Schamel‐KdV Equation

Dynamics of a stochastic SIS epidemic model with nonlinear incidence rates

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