Periodic bright–dark soliton, breather-like wave and rogue wave solutions to a $${\bar{p}}$$-GBS equation in (3+1)-dimensions

Gai, Litao; Qian, Youhua; Qin, Yupeng; Zhang, Runfa

doi:10.1007/s11071-023-08628-y

Cited by 4 publications

(2 citation statements)

References 27 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In addition, the crest of this breather waves appears periodically instead of breather solutions in [39]. It is interesting that the bright-dark solitons solution [40] have certain features in common with the solutions in figure 5, but they are also different in structures. To the best of our knowledge, those new results obtained has never been reported in the study of other variants of (2 + 1)-dimensional Ito equation.…”

Section: Discussionmentioning

confidence: 88%

Diversity of exact solutions to the (2+1)-dimensional Ito equation via bilinear neural network method

Ma,

Sudao

2023

Phys. Scr.

View full text Add to dashboard Cite

Recently, searching for exact solutions to nonlinear partial differential equations has gradually become a hot research topic. It is of great scientific research and application value to reveal the law of wave propagation, explain natural phenomena accurately and apply related technologies scientifically. In this paper, bilinear neural network method (BNNM) was employed to obtain some new exact analytical solutions to the (2 + 1)-dimensional Ito equation. Based on the Hirota form of Ito equation, we constructed activation functions f in various forms containing the exp(ξ), sin(ξ), cos(ξ), cosh(ξ) and squares of polynomial functions in multi-layer neurons such as [3-2-2] and [3-2-3] neural network models. The test function f in this work is a new expression. On the other hand, these solutions have not been studied yet. As a result, we obtained several new interaction solutions, such as periodic wave solution, breather solution and bright-dark solitons solution, etc. In addition, the corresponding 3D, density and contour plots of all the solution forms were drawn and their characters and dynamic behaviors were vividly demonstrated.

show abstract

Section: Discussionmentioning

confidence: 88%

Diversity of exact solutions to the (2+1)-dimensional Ito equation via bilinear neural network method

Ma,

Sudao

2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Consequently, many classic frameworks are based on a single hidden layer. The appeal of using neural network models to solve NLEEs lies in their robust nonlinear characteristics [22,23].…”

Section: Introductionmentioning

confidence: 99%

Multiple rogue wave solutions of the (1+1)-dimensional Benjamin-Ono equation

Ma,

Sudao,

Shao

2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, by means of symbolic computation, we studied the multiple rogue wave (multi-RW) solutions of the (1+1)-dimensional Benjamin-Ono (BO) equation, which is used to describe one-dimensional deep water internal waves in mathematics. In order to achieve this goal, we used the bilinear neural network method to construct the superposition formulas of n-RW based on the bilinear form. Here we only showed 1-RW, 3-RW, and 6-RW solutions. The influence of the parameters in the solution expression upon the characteristics related to RW also was discussed. Then, the dynamics characteristics of the multi-RW solutions were analyzed by drawing the three-dimensional plot, contour plot, and density plot. We observed that m-RW consisted of m independent 1-RW. This interesting phenomenon helped us to better reveal the evolution mechanism of the (1+1)-dimensional BO equation.

show abstract

N-solitons, lump-stripe solitons with inelastic collisions and new periodic rogue waves of a (2+1)-dimensional extended Sawada–Kotera equation

Gai,

Xu,

Zhang

2024

Nonlinear Dyn

View full text Add to dashboard Cite

Periodic bright–dark soliton, breather-like wave and rogue wave solutions to a $${\bar{p}}$$-GBS equation in (3+1)-dimensions

Cited by 4 publications

References 27 publications

Diversity of exact solutions to the (2+1)-dimensional Ito equation via bilinear neural network method

Diversity of exact solutions to the (2+1)-dimensional Ito equation via bilinear neural network method

Multiple rogue wave solutions of the (1+1)-dimensional Benjamin-Ono equation

N-solitons, lump-stripe solitons with inelastic collisions and new periodic rogue waves of a (2+1)-dimensional extended Sawada–Kotera equation

Contact Info

Product

Resources

About