Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

Qiao, Ji‐Mei; Zhang, Runfa; Yue, Rong‐Xian; Rezazadeh, Hadi; Seadawy, Aly R.

doi:10.1002/mma.8131

Cited by 26 publications

(4 citation statements)

References 42 publications

(74 reference statements)

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“…Using both the modified hyperbolic tangent function method and different parameters, Duan et al obtained three kinds of exact solutions of equation (3) [36]. Based on the Hirota bilinear method, Qiao et al searched for some analytical solutions for a new (3+1)-dimension BLMP equation [39]. In [40], the exact closed-form solutions were constructed for equation (3) by the generalized exponential rational function method.…”

Section: Introductionmentioning

confidence: 99%

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

He,

Han,

et al. 2024

Phys. Scr.

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Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.

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Section: Introductionmentioning

confidence: 99%

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

He,

Han,

et al. 2024

Phys. Scr.

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“…Due to the strong nonlinear characteristics of neural network models, the application of neural network models in solving NLEEs has attracted the attention of researchers. Three types of periodic solutions to new (3 + 1)-dimensional Boiti-Leon-Manna-Pempinelli equation were obtained in [29]. Reference [30] has constructed various solutions to the (2 + 1)-dimensional Hirota-Satsuma-Ito equation, such as breathers, interaction of rogue wave and soliton, traveling waves and rogue waves.…”

Section: Introductionmentioning

confidence: 99%

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

Ma,

Sudao

2023

Phys. Scr.

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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.

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“…In addition, Zhang et al used this method to obtain exact analytical solutions of many NLPDEs, such as the p-gBKP equation [55,56], the gBS equation [57], the SK-like equation [58], the CDGKSlike equation [59]. And there are scholars interested in this approach, such as Qiao et al and Shen et al used BNNM to obtain three types of periodic solutions [60] and periodic-soliton [61] for BMLP equation. Zeynel et al used BNNM to obtain a rogue, bright and dark wave solutions for a Hirota type equation [62].…”

Section: Introductionmentioning

confidence: 99%

A governing equation of Rossby waves and its dynamics evolution by Bilinear neural network method

et al. 2023

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This paper studies an extended evolution equation of large-scale waves by means of bilinear neural network method, which is obtained from local Cartesian coordinate system of the basic equation set by using scaling analysis method and perturbation expansions method. First, we convert the equation into a Hirota equation by using variable transformation. Then, we give the structure framework and the model of the bilinear neural network. We build the test function in two dimensions: depth and breadth. With choosing appropriate activation functions and neuron coefficients, we get many rational function exact solutions, including rogue waves and interaction phenomenon consisting of rogue wave and soliton wave. At last, the figures of these exact solutions are exhibited by selecting suitable value of parameters. We think that these results are very important in ocean dynamics.

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Three types of periodic solutions of new (3 + 1)‐dimensional Boiti–Leon–Manna–Pempinelli equation via bilinear neural network method

Cited by 26 publications

References 42 publications

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

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

A governing equation of Rossby waves and its dynamics evolution by Bilinear neural network method

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