Elastic and nonelastic interactional solutions for the (2 + 1)-dimensional Ito equation

Zhou, Ai-Juan; Lan, Lan

doi:10.1080/25765299.2019.1576583

Cited by 4 publications

(1 citation statement)

References 27 publications

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“…Tang et al [10] presented two classes of lump and interaction solutions, which included rational, periodic, and hyperbolic functions. Zhou and Lan [11] derived nonelastic interactional solutions composed of three different types of waves by two new test functions and the bilinear form. Du and Lou [12] investigated the interactions of lump and solitons.…”

Section: Introductionmentioning

confidence: 99%

Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation

Zhu,

Liu,

Arefin

et al. 2023

Advances in Mathematical Physics

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In this work, a (2 + 1)-dimensional Ito equation is investigated, which represents the generalization of the bilinear KdV equation. Abundant double-periodic soliton solutions to the (2 + 1)-dimensional Ito equation are presented by the Hirota bilinear form and a mixture of exponentials and trigonometric functions. The dynamic properties are described through some 3D graphics and contour graphics.

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Section: Introductionmentioning

confidence: 99%

Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation

Zhu,

Liu,

Arefin

et al. 2023

Advances in Mathematical Physics

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Dynamics of closed-form invariant solutions and diversity of wave profiles of (2+1)-dimensional Ito integro-differential equation via Lie symmetry analysis

Kumar

Hamid

2022

Journal of Ocean Engineering and Science

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High-dimensional nonlinear wave transitions and their mechanisms

Zhang

Wang

Liu

et al. 2020

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, the dynamics of transformed nonlinear waves in the (2+1)-dimensional Ito equation are studied by virtue of the analysis of characteristic line and phase shift. First, the N-soliton solution is obtained via the Hirota bilinear method, from which the breath-wave solution is derived by changing values of wave numbers into complex forms. Then, the transition condition for the breath waves is obtained analytically. We show that the breath waves can be transformed into various nonlinear wave structures including the multi-peak soliton, M-shaped soliton, quasi-anti-dark soliton, three types of quasi-periodic waves, and W-shaped soliton. The correspondence of the phase diagram for such nonlinear waves on the wave number plane is presented. The gradient property of the transformed solution is discussed through the wave number ratio. We study the mechanism of wave formation by analyzing the nonlinear superposition between a solitary wave component and a periodic wave component with different phases. The locality and oscillation of transformed waves can also be explained by the superposition mechanism. Furthermore, the time-varying characteristics of high-dimensional transformed waves are investigated by analyzing the geometric properties (angle and distance) of two characteristic lines of waves, which do not exist in (1+1)-dimensional systems. Based on the high-order breath-wave solutions, the interactions between those transformed nonlinear waves are investigated, such as the completely elastic mode, semi-elastic mode, inelastic mode, and collision-free mode. We reveal that the diversity of transformed waves, time-varying property, and shape-changed collision mainly appear as a result of the difference of phase shifts of the solitary wave and periodic wave components. Such phase shifts come from the time evolution as well as the collisions. Finally, the dynamics of the double shape-changed collisions are presented.

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Elastic and nonelastic interactional solutions for the (2 + 1)-dimensional Ito equation

Cited by 4 publications

References 27 publications

Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation

Double-Periodic Soliton Solutions of the (2+1)-Dimensional Ito Equation

Dynamics of closed-form invariant solutions and diversity of wave profiles of (2+1)-dimensional Ito integro-differential equation via Lie symmetry analysis

High-dimensional nonlinear wave transitions and their mechanisms

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