Kadomtsev–Petviashvili equation in relativistic fluid dynamics

Fogaça, D. A.; Navarra, F. S.; Filho, L. G. Ferreira

doi:10.1016/j.cnsns.2012.07.006

Cited by 11 publications

(24 citation statements)

References 43 publications

(81 reference statements)

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“…Consider N independent variable such as X = (X 1 , X 2 , … , X N ) and U = (U 1 , U 2 , … , U M ), be M dependent variables. Take into consideration, also a system of R PDEs with K th −order as 35 Q [U] = Q (X, U, U (1) , U (2) , … , U (K) ), = 1, 2, … , R,…”

Section: Conservation Laws For Equation (1) By Multipliermentioning

confidence: 99%

“…In recent years, studies on nonlinear evolution equations (NLEE) are devoted to investigate various phenomena in nonlinear science. Focusing attention on different branches, such as fluid mechanics, plasma physics, chemistry, biology, solid‐state materials, etc . To this issue , various methods were suggested in the literature in the last few decades.…”

Section: Introductionmentioning

confidence: 99%

“…Focusing attention on different branches, such as fluid mechanics, plasma physics, chemistry, biology, solid-state materials, etc. [1][2][3][4][5] To this issue , various methods were suggested in the literature in the last few decades. With relevance to multiwave solutions.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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In this article, the generalized unified method (GUM) is used for finding multiwave solutions of the coupled Whitham‐Broer‐Kaup (WBK) equation with variable coefficients. Which describes the propagation of of shallow water waves. Here, we study the effects of the indirect nonlinear interaction of one‐, two‐ and three‐solitonic similaritons on the behavior of propagation of waves, in quasi‐periodic distributed system. This study can unable us to control the dynamics of type soliton (soliton, anti‐soliton) similaritons waves in dispersive waveguides. To give more physical insight to the obtained solutions, they are shown graphically. Their different structures are depicted by taking appropriate arbitrary functions. Further, with the suitable parameters, the indirect nonlinear interaction between two and three‐soliton waves are shown weal, in the sense that their amplitude does not blow up. Moreover, because of the importance of conservation laws Cls and stability analysis SA in the investigation of integrability, internal properties, existence, and uniqueness of a differential equation, we compute the Cls via multiplier technique and stability analysis via the concept of linear stability analysis for the WBK equations using the constant coefficients.

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Section: Conservation Laws For Equation (1) By Multipliermentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Abdel‐Gawad

Tantawy

Yusuf

2019

Math Methods in App Sciences

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show abstract

“…We next combine (50) and (5) to obtain a nonlinear wave equation. In dealing with these equations we use the reductive perturbation method (RPM) [33][34][35][36][37][38], which is a technique which allows us to go beyond linearization and to preserve nonlinearities, dissipative and dispersive terms in the wave equations. We have already used the RPM in our previous works to study nonlinear waves in relativistic and nonrelativistic ideal hydrodynamics and also to study the evolution of flux in relativistic viscous hydrodynamics [24].…”

Section: B Nonlinear Waves In a Hadron Gasmentioning

confidence: 99%

“…We will later go beyond linearization and study the effects of viscosity on the propagation of nonlinear waves. To this end, we employ the well-established reductive perturbation method (RPM) [33][34][35][36][37][38].…”

Section: Introductionmentioning

confidence: 99%

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

2013

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We study linear and nonlinear wave propagation in a dense and cold hadron gas and also in a cold quark-gluon plasma, taking viscosity into account and using the Navier-Stokes equation. The equation of state of the hadronic phase is derived from the nonlinear Walecka model in the mean-field approximation. The quark-gluon plasma phase is described by the MIT equation of state. We show that in a hadron gas viscosity strongly damps wave propagation and also hinders shock-wave formation. This marked difference between the two phases may have phenomenological consequences and lead to new quark-gluon plasma signatures.

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Nonlinear dynamic behaviors of the generalized (3+1)‐dimensional KP equation

et al. 2022

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Under investigation in this article is a generalized (3+1)‐dimensional Kadomtsev–Petviashvili (KP) equation, which is usually used to describe nonlinear phenomena in fluid dynamics. First, multiple waves solutions of this considered equation by means of the linear superposition principle are constructed. Second, the parameters of this considered model control multiple waves solutions are being investigated. We find that the parameters mainly affect the wave shapes, amplitude, and bright/dark nature. Third, we apply a polynomial function to construct rational solutions and rogue wave solutions when the parameters contain in the polynomial function are equal to zero and nonzero, respectively. Finally, the obtained results are demonstrated graphically to illustrate the nonlinear dynamics behaviors of multiple, rational, and rogue wave solutions in fluid mechanics.

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Kadomtsev–Petviashvili equation in relativistic fluid dynamics

Cited by 11 publications

References 43 publications

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

On multiple soliton similariton‐pair solutions, conservation laws via multiplier and stability analysis for the Whitham–Broer–Kaup equations in weakly dispersive media

Viscosity, wave damping, and shock-wave formation in cold hadronic matter

Nonlinear dynamic behaviors of the generalized (3+1)‐dimensional KP equation

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