Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation

Jhangeer, Adil; Hussain, Amjad; Junaid-U-Rehman, M.; Khan, İlyas; Băleanu, Dumitru; Nisar, Kottakkaran Sooppy

doi:10.1016/j.rinp.2020.103492

Cited by 39 publications

(7 citation statements)

References 30 publications

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“…Symmetry reduction and differential invariants for equation (1) Z = {Z 1 , Z 2 , Z 3 } forms an abelian sub algebra which can be represented in table 1. One dimensional optimal system for Z [55,57] is:…”

Section: Travelling Wave Patternsmentioning

confidence: 99%

Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis

et al. 2021

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In this work, the tanh method is employed to compute some traveling wave patterns of the nonlinear third-order (2+1) dimensional Chaffee-Infante (CI) equation. The tanh technique is successfully used to get the traveling wave solutions of a considered model in the form of some hyperbolic functions. The Lie symmetry technique is used to analyze the Chaffee-Infante (CI) equation and compute the Infinitesimal generators under the invariance criteria of Lie groups. Then we construct the commutator table, adjoint representation table, and we have represented symmetry groups for each Infinitesimal generator. The optimal system and similarity reduction method is used to obtain some analytical solutions of the considered model. With the help of the similarity reduction method, we have converted the nonlinear partial differential equation into nonlinear ordinary differential equations (ODEs). Moreover, we have shown graphically obtained wave solutions by using the different values of involving parameters. Conserved quantities of nonlinear CI equation are obtained by the multiplier approach.

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Section: Travelling Wave Patternsmentioning

confidence: 99%

Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis

et al. 2021

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“…The Lie symmetry analysis approach [1][2][3][4][5][6][7][8] has many applications in different fields, including physics, engineering, and mathematical modeling. It can be used to study a wide range of nonlinear PDEs, including those that are difficult to solve using other methods.…”

Section: Introductionmentioning

confidence: 99%

Conservation Laws, Solitary Wave Solutions, and Lie Analysis for the Nonlinear Chains of Atoms

Rehman

Awrejcewicz

Kudra

2023

Preprint

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Nonlinear chains of atoms(NCA) are complex systems with rich dynamics, influencing various scientific disciplines. Lie symmetry approach is considered to analyze the NCA. The Lie symmetry method is a powerful mathematical tool for analyzing and solving differential equations with symmetries, facilitating the reduction of complexity and obtaining solutions. After getting the entire vector field by using the Lie scheme, we find the optimal system of symmetries. Using the optimal system we have converted assumed PDE into nonlinear ODE. The new auxiliary scheme introduces novel approaches to complement existing techniques, enhancing accuracy and simplifying computations. Travelling wave solutions describe wave-like propagation in systems, while graphical behavior visually represents relationships and patterns in data or mathematical models. The multiplier method enables the identification of conservation laws, fundamental principles in physics that assert certain quantities remain constant over time. Understanding these concepts contributes to a deeper comprehension of nonlinear chains of atoms and their dynamics, fostering advancements in related fields.

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“…One of the earliest studies was done by Gazizov et al [21], by extending the Lie symmetry approach for FPDEs, and proposed prolongation formulae for fractional derivatives. Later, many researchers apply this approach for such type of time-fractional equation, particularly Riemann-Liouville derivative; see [22][23][24][25][26][27][28]. The popular work of Noether, known as Noether theorem [29], describes the linkage with symmetry of the Euler-Lagrange equation and conservation laws.…”

Section: Introductionmentioning

confidence: 99%

Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation

Bahi

Hilal

2022

Advances in Mathematical Physics

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In this paper, Lie symmetries of time-fractional KdV-Like equation with Riemann-Liouville derivative are performed. With the aid of infinitesimal symmetries, the vector fields and symmetry reductions of the equation are constructed, respectively; as a result, the invariant solutions are acquired in one case; we show that the KdV-like equation can be reduced to a fractional ordinary differential equation (FODE) which is connected with the Erdélyi-Kober functional derivative; for this kind of reduced form, we use the power series method for extracting the explicit solutions in the form of power series solution. Finally, Ibragimov’s theorem has been employed to construct the conservation laws.

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Lie analysis, conservation laws and travelling wave structures of nonlinear Bogoyavlenskii–Kadomtsev–Petviashvili equation

Cited by 39 publications

References 30 publications

Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis

Some exact explicit solutions and conservation laws of Chaffee-Infante equation by Lie symmetry analysis

Conservation Laws, Solitary Wave Solutions, and Lie Analysis for the Nonlinear Chains of Atoms

Symmetry Analysis, Invariant Solutions, and Conservation Laws of Fractional KdV-Like Equation

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