Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

Ali, Mohamed R.

doi:10.4208/eajam.100920.060121

Cited by 25 publications

(13 citation statements)

References 22 publications

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“…The traveling wave solutions can not be acquired since the dBKP system has the characteristic that each term contains the first power factor of the same order without dispersion term. Compared with other published papers on the study related to B-type equations [25][26][27][28], the current paper adds the application of symmetry analysis on the dispersionless B-type equation. Further research on obtained Lie point symmetries and special symmetry reductions by -symmetry [29], Laplace transform [30] and PT-symmetry [31] are worth trying in the future.…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Lie Symmetry Analysis and Conservation Laws for the (2 + 1)-Dimensional Dispersionless B-Type Kadomtsev–Petviashvili Equation

Zhao

Wang

et al. 2022

J Nonlinear Math Phys

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The Lie symmetry analysis is adopted to the (2 + 1)-dimensional dispersionless B-type Kadomtsev–Petviashvili (dBKP) equation. The combination of symmetry analysis and symbolic computing methods proves that Lie algebra of infinitesimal symmetry of the dBKP equation depends on four independent arbitrary functions and one arbitrary parameter. The Lie algebra is reduced to four classes for deriving commutative relations, group invariant solutions of dBKP equation and conservation laws, and the optimal system of 1-dimensional subalgebras from one class is constructed. Based on the optimal system and other particular infinitesimal symmetries, plentiful symmetry reductions and invariant solutions are computed by using Lie group method. Six successive symmetries and conserved quantities of the dBKP equation are linked by the new conservation theorem. Besides, exact solution of the dBKP equation is constructed according to a conservation vector.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Lie Symmetry Analysis and Conservation Laws for the (2 + 1)-Dimensional Dispersionless B-Type Kadomtsev–Petviashvili Equation

Zhao

Wang

et al. 2022

J Nonlinear Math Phys

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show abstract

“…Lie group analysis is used in many dierent elds such as control theory, algebraic topology,dierential geometry,relativity [1], physics [2,3,4,5,6,7,8], geometry, mechanics [9], Chemistry and Chemical biology [10]. Moreover it has been used in mathematical models such as models regarding deceases [11,12,13], models of epidemics [14] and nance [15,16].…”

Section: Introductionmentioning

confidence: 99%

“…For formulating mathematical models, engineering problems and physical problems, Nonlinear ordinary dierential equations (NODEs) are used widely [18] [2]. Nevertheless, explicit solutions can be obtained for very few NODEs [19].…”

Section: Introductionmentioning

confidence: 99%

“…Therefore above rotations can be considered as discrete symmetries of the equilateral triangle. Consider a unit circle given by cos(θ) 2 + sin(θ) 2 = 1. Then a rotation of ε ∈ (−π, π] angel around the center is a symmetry and it can be represented by cos(θ + ε) 2 + sin(θ + ε) 2 = 1.…”

Section: Introductionmentioning

confidence: 99%

“…Consider a unit circle given by cos(θ) 2 + sin(θ) 2 = 1. Then a rotation of ε ∈ (−π, π] angel around the center is a symmetry and it can be represented by cos(θ + ε) 2 + sin(θ + ε) 2 = 1. This transformation can be considered as a continuous symmetry since ε can be varied continuously i.e ε ∈ (−π, π].…”

Section: Introductionmentioning

confidence: 99%

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Solution Methods for Nonlinear Ordinary Differential Equations Using Lie Symmetry Groups

Perera

Gallage²

2023

Adv. J. Grad. Res.

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For formulating mathematical models, engineering problems and physical problems, Nonlinear ordinary differential equations(NODEs) are used widely. Nevertheless, explicit solutions can be obtained for very few NODEs, due to lack of techniques to obtain explicit solutions. Therefore methods to obtain approximate solution for NODEs are used widely. Although symmetry groups of ordinary differential equations (ODEs) can be used to obtain exact solutions however, these techniques are not widely used. The purpose of this paper is to present applications of Lie symmetry groups to obtain exact solutions of NODEs . In this paper we connect different methods,theorems and definitions of Lie symmetry groups from different references and we solve first order and second order NODEs. In this analysis three different methods are used to obtain exact solutions of NODEs. Using applications of these symmetry methods, drawbacks and advantages of these different symmetry methods are discussed and some examples have been illustrated graphically. Focus is first placed on discussing about the notion of symmetry groups of the ODEs. Focus is then changed to apply them to find general solutions for NODEs under three different methods. First we find suitable change of variables that convert given first order NODE into variable separable form using these symmetry groups. As another method to find general solutions for first order NODEs, we find particular type of solution curves called invariant solution curves under Lie symmetry groups and we use these invariant solution curves to obtain the general solutions. We find general solutions for the second order NODEs by reducing their order to first order using Lie symmetry groups.

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Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation

Simon,

Bira

2024

Math Methods in App Sciences

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In this article, we consider a nonlinear time‐fractional foam drainage equation and investigate the behavior of fluid flow through the foam. First, we apply the symmetry analysis and obtain the infinitesimal group of transformations involving some arbitrary parameters. Further, we classify the one‐dimensional optimal algebra, and using that, we obtain the similarity variables, which consequently reduces the time fractional partial differential equation (FPDE) to fractional‐order ordinary differential equation (FODE). Next, under the invariance condition, we construct exact solution for the given model and presented graphically. Furthermore, we derive the two‐dimensional optimal systems and nonclassical symmetry for the governing equation. Finally, we study the nature of fluid flow through the foam by numerical simulation.

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Lie Symmetry Analysis and Wave Propagation in Variable-Coefficient Nonlinear Physical Phenomena

Cited by 25 publications

References 22 publications

Lie Symmetry Analysis and Conservation Laws for the (2 + 1)-Dimensional Dispersionless B-Type Kadomtsev–Petviashvili Equation

Lie Symmetry Analysis and Conservation Laws for the (2 + 1)-Dimensional Dispersionless B-Type Kadomtsev–Petviashvili Equation

Solution Methods for Nonlinear Ordinary Differential Equations Using Lie Symmetry Groups

Lie Symmetries With Exact Solution for Time‐Fractional Foam Drainage Equation

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