Bäcklund transformation and soliton solutions in terms of the Wronskian for the Kadomtsev–Petviashvili-based system in fluid dynamics

Du, Zhong; Tian, Bo; Xie, Xin; Chai, Jun; Wu, Xiao-Yu

doi:10.1007/s12043-018-1532-2

Cited by 30 publications

(8 citation statements)

References 30 publications

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“…While there is a gap in the Wu-Zhang system's harmonious time zone literature, the classical Wu-Zhang system is thought to have achieved soliton solutions by many researchers [35,36,37]. In recent years, this system of equations has been discussed by many researchers to …nd exact solutions of di¤erent types.…”

Section: Wu-zhang System With Conformable Derivativementioning

confidence: 99%

The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

Kaplan

Akbulut

2021

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Section: Wu-zhang System With Conformable Derivativementioning

confidence: 99%

The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

Kaplan

Akbulut

2021

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“…Therefore, the research on solving methods for the NPDEs remains a key and difficult topic in the field of nonlinear scientific research. So far, a good many effective and reliable approaches have emerged to deal with the NPDEs, for example the Darboux transformation approach [13][14][15], direct algebraic approach [16,17], variational technique [18], Bäcklund transformation method [19][20][21], subequation method [22][23][24], tanhfunction method [25,26], exp-function approcah [27,28], generalised exponential rational function approach [29,30] and many others [31][32][33][34][35][36][37][38]. Under the current work, we are going to inquire into the extended (3+1)dimensional JME that is given by [39]:…”

Section: Introductionmentioning

confidence: 99%

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Wang

2024

Phys. Scr.

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The central purpose of this paper is extracting some novel and interesting soliton solutions of the extended (3+1)-dimensional Jimbo-Miwa equation(JME) which acts as an extension of the classic (3+1)-dimensional JME for the plasma and optics. First, we study the N-soltion solutions that is developed by the Hirota bilinear method (HBM). Then, the soliton molecules and Y-type soliton solutions are constructed via imposing the novel resonance conditions to the N-soltion solutions. In addition, we also explore the complex multiple soliton solutions via the HBM. The dynamic properties of the N-soltion, soliton molecules, Y-type soliton as well as the complex multiple soliton solutions are presented graphically. The developed soliton solutions of this research are all new and can enable us apprehend the nonlinear dynamic behaviors of the extended (3+1)-dimensional JME better.

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“…How to obtain the exact solution of the NPDEs has always been the purpose of researchers. To this day, some effective methods have been proposed to seek for the exact solution of the NPDEs such as the Bäcklund transformation method [7][8][9][10], Cole-Hopf transformation method [11][12][13][14], variational method [15,16], extended rational sinecosine and sinh-cosh methods [17,18], Sardar subequation method [19,20], the Kudryashov approach [21,22], extended sinh-Gordon equation expansion method [23,24], trial equation method [25,26], sub-equation method [27][28][29], Wang's direct mapping method [30], and so on [31][32][33][34][35]. In this work, we aim to study the (3+1)-dimensional B-type Kadomtsev-Petviashvili equation that reads as [36]:…”

Section: Introductionmentioning

confidence: 99%

Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics

Wang

Liu

et al. 2023

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This paper provides an investigation on nonlinear dynamic behaviors of the (3+1)-dimensional B-type Kadomtsev—Petviashvili equation, which is used to model the propagation of weakly dispersive waves in a fluid. With the help of the Cole—Hopf transform, the Hirota bilinear equation is established, then the symbolic computation with the ansatz function schemes is employed to search for the diverse exact solutions. Some new results such as the multi-wave complexiton, multi-wave, and periodic lump solutions are found. Furthermore, the abundant traveling wave solutions such as the dark wave, bright-dark wave, and singular periodic wave solutions are also constructed by applying the sub-equation method. Finally, the nonlinear dynamic behaviors of the solutions are presented through the 3-D plots, 2-D contours, and 2-D curves and their corresponding physical characteristics are also elaborated. To our knowledge, the obtained solutions in this work are all new, which are not reported elsewhere. The methods applied in this study can be used to investigate the other PDEs arising in physics.

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Bäcklund transformation and soliton solutions in terms of the Wronskian for the Kadomtsev–Petviashvili-based system in fluid dynamics

Cited by 30 publications

References 30 publications

The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

The analysis of the soliton-type solutions of conformable equations by using generalized Kudryashov method

Soliton molecules, Y-type soliton and complex multiple soliton solutions to the extended (3+1)-dimensional Jimbo-Miwa equation

Nonlinear Dynamic Behaviors of the (3+1)-Dimensional B-Type Kadomtsev—Petviashvili Equation in Fluid Mechanics

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