Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach

Devi, Munesh; Yadav, Shalini; Arora, Rajan

doi:10.1016/j.amc.2021.126230

Cited by 19 publications

(7 citation statements)

References 44 publications

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“…a a a a a a a a = we obtain the following system of algebraic equations [28,29] ˜( ) e e e , , , The optimal system for vcCBE is discussed below.…”

Section: Optimal Systemmentioning

confidence: 99%

The Lie symmetry analysis and dynamics of exact solutions for variable coefficients (2+1)-dimensional coupled burgers equation

Liu¹,

Yan²,

Meng³

et al. 2022

Phys. Scr.

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In this article, the (2+1)-dimensional variable coefficients coupled Burgers equation (vcCBE) is investigated for the first time with the help of Lie symmetry analysis method. This equation is an important nonlinear physical model. The optimal system of the (2+1)-dimensional vcCBE is analyzed by Olver’s method. Then, the (2+1)-dimensional vcCBE is reduced on the basis of the optimal system to multiple sets of (1+1)-dimensional equations. Various types of soliton solutions are obtained by solving the reduced equations. The G ′ / G -expansion method, tanh-coth method, and Riccati equation method are used respectively. Finally, the obtained solutions are analyzed dynamically and their kinetic behavior is investigated.

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“…a a a a a a a a = we obtain the following system of algebraic equations [28,29] ˜( ) e e e , , , The optimal system for vcCBE is discussed below.…”

Section: Optimal Systemmentioning

confidence: 99%

The Lie symmetry analysis and dynamics of exact solutions for variable coefficients (2+1)-dimensional coupled burgers equation

Liu¹,

Yan²,

Meng³

et al. 2022

Phys. Scr.

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“…The nonlinear evolution equations are the key to examine and analyze problems found in numerous fields like biology, zoology, physics, chemistry, optics, fluid mechanics and geophysics. A variety of nonlinear models are investigated by different researchers like nonlinear Schrödinger equation [ 1 – 3 ], geophysical Korteweg-de Vries equation [ 4 ], Ablowitz-Kaup-Newell-Segur equation [ 5 ], (3 + 1)sine-Gordon equation [ 6 ] and many other equations. Various models are examined in detail for deriving soliton solutions [ 7 – 10 ].…”

Section: Introductionmentioning

confidence: 99%

Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

et al. 2023

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This article deals with studying the dynamical behavior of the DNA model proposed by Peyrard and Bishop. The proposed model is investigated using the unified method (UM). Unified method successfully extracts solutions in the form of polynomial and rational functions. The solitary wave solutions and soliton solutions are constructed. An investigation of modulation instability is also presented in this paper. 3D and 2D plots are presented to exhibit the physical behavior of some of the obtained solutions.

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“…These solutions are essential for seeing how integrated physical phenomena work inside. For obtaining optical solutions for NLPDEs, numerous significant strategies have been proposed, including the modified polynomial expansion technique [11], the enhanced [12], the exp − ð ϕ ξ ð ÞÞ-expansion technique [13], the generalized Kudryashov approach [14], the new auxiliary equation technique [15], the lie symmetry approach [16], the extended Fan subequation technique [17], the complex technique [18], the improved Bernoulli subequation approach [19], and so on.…”

Section: Introductionmentioning

confidence: 99%

Soliton Solutions to the BA Model and (3 + 1)‐Dimensional KP Equation Using Advanced exp(−ϕ(ξ))‐Expansion Scheme in Mathematical Physics

Mawa,

Islam,

Bashar

et al. 2023

Mathematical Problems in Engineering

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In this manuscript, the primary motivation is the implementation of the advanced exp − ϕ ξ -expansion method to construct the soliton solution, which contains some controlling parameters of two distinct equations via the Biswas–Arshed model and the (3 + 1)-dimensional Kadomtsev–Petviashvili equation. Here, the solutions’ behaviors are presented graphically under some conditions on those parameters. The height of the wave, wave direction, and angle of the obtained wave is formed by substituting the particular values of the considerations over showing figures with the control plot. With the collaboration of the advanced exp − ϕ ξ -expansion method, we construct entirely the solitary wave results as well as rogue type soliton, combined singular soliton, kink, singular kink, bright and dark soliton, periodic shape, double periodic shape soliton, etc. Therefore, it is remarkable to perceive that the advanced exp − ϕ ξ -expansion technique is a simple, viable, and numerical solid apparatus for clarifying careful outcomes to the other nonstraight equivalences.

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Optimal system, invariance analysis of fourth-Order nonlinear ablowitz-Kaup-Newell-Segur water wave dynamical equation using lie symmetry approach

Cited by 19 publications

References 44 publications

The Lie symmetry analysis and dynamics of exact solutions for variable coefficients (2+1)-dimensional coupled burgers equation

The Lie symmetry analysis and dynamics of exact solutions for variable coefficients (2+1)-dimensional coupled burgers equation

Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

Soliton Solutions to the BA Model and (3 + 1)‐Dimensional KP Equation Using Advanced exp(−ϕ(ξ))‐Expansion Scheme in Mathematical Physics

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