Lie symmetry analysis, soliton solutions and qualitative analysis concerning to the generalized q-deformed Sinh-Gordon equation

Raza, Nauman; Salman, Farwa; Butt, Asma Rashid; Gandaria, Maria Luz

doi:10.1016/j.cnsns.2022.106824

Cited by 73 publications

(12 citation statements)

References 36 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…method, it is imperative that we initially ascertain the value of N = 1 by making use of the homogeneous balancing principle. This process involves comparing the terms 'u raised to the power of 4' and u raised to the power of 5 as derived from equation (23):…”

Section: Solutions By Extended ( ) ¢ G G 2 -Expansion Techniquementioning

confidence: 99%

“…Such solutions have the potential to offer valuable insights into the behavior exhibited by physical systems. These techniques include extended ( ) ¢ G G -expansion method [1], extended tanh-function method [2], exp-function method [3], F-expansion method [4], extended auxiliary equation method [5], Hirota's bilinear method [6], Kudryashov method [7], unified method [8,9], tanhfunction method [10,11], the ansatz method [12], the Backlund transformation [13][14][15][16], the sine-cosine method [17,18], the Jacobi elliptic function expansion method [19][20][21], Lie symmetry method [22][23][24] and many more. Because they represent confined waves that keep their shape while they propagate through a material, soliton solutions are particularly important in the field of physics.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Exact solutions and modulation instability analysis of a generalized Kundu-Eckhaus equation with extra-dispersion in optical fibers

Hussain,

Asif Ali Shah,

Naveed Rafiq

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

This study aims to examine the nonlinear partial differential equation known as the (1+1)-dimensional generalized Kundu-Eckhaus equation with extra-dispersion, which is used to model the transmission of ultra-short femtosecond pulses in an optical fiber. Two versatile techniques, namely the extended $(\frac{G'}{G^{2}})$-expansion as well as the extended $\exp(-\phi(\xi))$-expansion techniques, are utilized to generate numerous precise answers. Diverse novel collections of exact traveling wave solutions, such as bright solitons, dark solitons, singular solitons, W-shape solutions, M-shape solutions, and rational solutions, are identified as a result.Several of the acquired solutions are interpreted physically through the use of figures. In addition, the modulation instability analysis of the considered equation is performed and presented via 3D and 2D graphs.In the field of nonlinear sciences, the proposed methods have great value and can be applied to other nonlinear evolutionary equations that are used to represent nonlinear physical models.

show abstract

Section: Solutions By Extended ( ) ¢ G G 2 -Expansion Techniquementioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Exact solutions and modulation instability analysis of a generalized Kundu-Eckhaus equation with extra-dispersion in optical fibers

Hussain,

Asif Ali Shah,

Naveed Rafiq

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The deformation parameter q shows in the potential part of the equation, which is the generalization of the Sinh-Gordon equation. Analysis of Lie symmetry, soliton solutions, and qualitative analysis related to the generalized q-deformed Sinh-Gordon equation have already been covered by Raza et al [29]. In this work, we examine the generalized q-deformed Sinh-Gordon equation equation that is:…”

Section: Introductionmentioning

confidence: 99%

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Raza,

Arshed,

Ali Shah

et al. 2024

Phys. Scr.

Self Cite

View full text Add to dashboard Cite

This article deals with a new version of the generalized Q-deformedSinh-Gordon equation. Numerous physical interpretations and applications exist for the said model in several scientific fields. Therefore, in order to obtain a better understanding of the underlying physical system, it is imperative to look at the traveling wave behavior displayed by this equation. To complete our thrust three innovative integration architectures including the modified sub-equation method, the $G'/(bG'+G+a)$-expansion method and $\frac{G'}{G^{2}}$-expansion method have been utilized to createprecise closed form traveling wave solutions. These methods provide solutions in the form of hyperbolic function solutions, trigonometric function solutions and rational solutions. The obtained solutions are discussed with $3D$ surface plots and $2D$line plots to visualize and support the theoretical results. Furthermore, stability analysis of the proposed model is also carried out. This paper discusses a major development as well as gradual improvements to previous works on the current model. Moreover, we discuss the stability analysis of the studied equation and the outcomes are visually depicted in graphical form. To authenticate the solutions provided in this manuscript, each solution undergoes a meticulous validation process by reintegrating it into the original model using computational software.

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%

Solution Methods for Nonlinear Ordinary Differential Equations Using Lie Symmetry Groups

Perera

Gallage²

2023

Adv. J. Grad. Res.

View full text Add to dashboard Cite

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.

show abstract

Lie symmetry analysis, soliton solutions and qualitative analysis concerning to the generalized q-deformed Sinh-Gordon equation

Cited by 73 publications

References 36 publications

Exact solutions and modulation instability analysis of a generalized Kundu-Eckhaus equation with extra-dispersion in optical fibers

Exact solutions and modulation instability analysis of a generalized Kundu-Eckhaus equation with extra-dispersion in optical fibers

Unveiling novel dynamics in Q-deformed Sinh-Gordon model: exploring explicit wave solutions and stability analysis

Solution Methods for Nonlinear Ordinary Differential Equations Using Lie Symmetry Groups

Contact Info

Product

Resources

About