On periodic wave solutions with asymptotic behaviors to a <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si44.gif" display="inline" overflow="scroll"><mml:mrow><mml:mo>(</mml:mo><mml:mn>3</mml:mn><mml:mo>+</mml:mo><mml:mn>1</mml:mn><mml:mo>)</mml:mo></mml:mrow></mml:math>-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics

Tu, Jian-Min; Tian, Shou‐Fu; Xu, Meijuan; Ma, Pan-Li; Zhang, Tiantian

doi:10.1016/j.camwa.2016.09.003

Cited by 92 publications

(17 citation statements)

References 30 publications

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“…where E is a polynomial of q. Taking c(t) � 1 and referring to the results presented in [44,45], we can get the form of the P-polynomials for equation (3) as follows:…”

Section: Bilinear Formmentioning

confidence: 99%

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Wang

2020

Complexity

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We investigate a reduced generalized (3 + 1)-dimensional shallow water wave equation, which can be used to describe the nonlinear dynamic behavior in physics. By employing Bell's polynomials, the bilinear form of the equation is derived in a very natural way. Based on Hirota's bilinear method, the expression of N-soliton wave solutions is derived. By using the resulting N-soliton expression and reasonable constraining parameters, we concisely construct the high-order breather solutions, which have periodicity in (x, y)-plane. By taking a long-wave limit of the breather solutions, we have obtained the high-order lump solutions and derived the moving path of lumps. Moreover, we provide the hybrid solutions which mean different types of combinations in lump(s) and line wave. In order to better understand these solutions, the dynamic phenomena of the above breather solutions, lump solutions, and hybrid solutions are demonstrated by some figures.

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“…where E is a polynomial of q. Taking c(t) � 1 and referring to the results presented in [44,45], we can get the form of the P-polynomials for equation (3) as follows:…”

Section: Bilinear Formmentioning

confidence: 99%

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Wang

2020

Complexity

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“…(3) were presented in [38,39]. Many methods have been applied to reach analytical solutions for PDEs [40][41][42][43][44][45][46][47]. The aim of this study is to analyze and investigate the LSA, explicit solution via the power series technique and Cls for Eq.…”

Section: Introductionmentioning

confidence: 99%

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

2018

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This article uses the extension of the Lie symmetry analysis (LSA) and conservation laws (Cls) (Singla et al. in Nonlinear Dyn. 89(1):321-331, 2017; Singla et al. in J. Math. Phys. 58:051503, 2017) for the space-time fractional partial differential equations (STFPDEs) to analyze the space-time fractional Rosenou-Haynam equation (STFRHE) with Riemann-Liouville (RL) derivative. We transform the space-time fractional RHE to a nonlinear ordinary differential equation (ODE) of fractional order using its Lie point symmetries. The reduced equation's derivative is in Erdelyi-Kober (EK) sense. We use the power series (PS) technique to derive explicit solutions for the reduced ODE for the first time. The Cls for the governing equation are constructed using a new conservation theorem.

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“…Authors of [5] obtained trawling wave solution for coupled Konno-Oono (CKO) equation using the modified exponential function method. A special case of system (1.1) to be considered transformed into new Konno-Oono equation system which is a coupled integrable dispersionless equations given as form of: )-expansion method [13][14][15], the G G ¢ -expansion method [16,17], the generalized G G ¢ -expansion method [18], the Bernoulli sub-equation function method [19][20][21][22], the sine-Gordon expansion method [23][24][25], the Ricatti equation expansion [26], the formal linearization method [27], the Lie symmetry [28][29][30], the Bäcklund transformations [31][32][33], the Darboux transformation [34], the Fokas method [35][36][37], the Hirota bilinear method [38][39][40][41]43], and so on.…”

Section: Introductionmentioning

confidence: 99%

On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method

Manafian

Zamanpour

2018

J. Phys. Commun.

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In this paper, the external trial equation method is employed to solve new coupled Konno-Oono (CKO) equation. By using this method, new exact solutions involving parameters, expressed by generalized hyperbolic and elleptic solutions are obtained. The current method presents a wider applicability for handling nonlinear wave equations. In addition, explicit new exact solutions are derived in different form such as dark solitons, bright solitons, solitary wave, periodic solitary wave, rational function, and elliptic function solutions of CKO equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena of this soliton wave equation.

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On periodic wave solutions with asymptotic behaviors to a (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics

Cited by 92 publications

References 30 publications

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

High-Order Breather Solutions, Lump Solutions, and Hybrid Solutions of a Reduced Generalized (3 + 1)-Dimensional Shallow Water Wave Equation

Space-time fractional Rosenou-Haynam equation: Lie symmetry analysis, explicit solutions and conservation laws

On some new analytical solutions for new coupled Konno–Oono equation by the external trial equation method

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