Lie analysis, conserved quantities and solitonic structures of Calogero-Degasperis-Fokas equation

Jhangeer, Adil; Rezazadeh, Hadi; Abazari, Reza; Yildirim, Kenan; Sharif, Sumaira; Ibraheem, Farheen

doi:10.1016/j.aej.2020.12.040

Cited by 16 publications

(3 citation statements)

References 58 publications

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“…A variety of methods have sprung up to solve nonlinear systems such as Lie symmetry analysis [1,19], Hirota bilinear method [3], conservation Laws [20][21][22][23], function cascade synchronization method [24], elliptic vortex ansatz [25] and so forth. The work of artificial neural network has made great progress for recent decades including the pattern recognition, intelligent robot, automation, forecast estimate, biology, medicine and other fields [26,27].…”

Section: Introductionmentioning

confidence: 99%

Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation

Feng

Bilige

2021

Phys. Scr.

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In this paper, we investigated various exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation in a mixture of liquid and gas bubbles. At first, the linear superposition principle was introduced to obtain resonant multi-soliton solutions and we took two cases as examples to illustrate the wave trajectories and the structure of resonant multi-soliton solutions through several sets of graphs. Next, multiple rogue wave solutions were derived via using the ‘4-2-4’ neural network model and we obtained its 1-rogue wave, 3-rogue wave and 6-rogue wave solutions through symbolic computation. In addition, three-dimensional, contour and density plots of multiple rogue wave solutions vividly shown their physical structure and dynamic properties. Furthermore, these solutions have greatly expanded the exact solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation on the available literature.

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Section: Introductionmentioning

confidence: 99%

Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation

Feng

Bilige

2021

Phys. Scr.

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“…Numerous strategies and their applications are accessible in the literature to compute the exact solutions of different classes of DEs that arise in numerous fields of science. There is no proficient and widespread methodology so far that a wide range of nonlinear equations can computed, for example the variational technique [8], ¢ G G-expansion technique [9,10], new extended direct algebraic technique [11], the asymptotic technique [12], the inverse scattering technique [13], the first integral method [14], soliton perturbation theory [15], and some other methods are represented in [16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Conserved quantities and travelling wave profiles to the nonlinear transmission line via Lie group analysis

Riaz¹,

Jhangeer²,

Abualnaja³

et al. 2021

Phys. Scr.

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The nonlinear transmission line (NLTL) equations are significant nonlinear evolution equations (NLEEs) in nonlinear electrical transmission line (NLETL) regulation. The tanh method is employed to compute some traveling wave patterns of the NLTL equation. The new extended direct algebraic method (NEDAM) is a viable and successful mathematical method to construct the traveling wave patterns of science and engineering problems. The NEDAM is effectively utilized to obtain the traveling wave structures of a considered model in the form of trigonometric and hyperbolic functions containing parameters. The Lie symmetry technique is used to analyze the NLTL equation and compute the Infinitesimal generators. Moreover, we have shown graphically obtained wave profiles by using the different suitable values of the parameters involved. Further, the nonlinear transmission line equation is described through nonlinear self-adjointness, and conserved quantities are computed for each vector.

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“…Saba et al [20] conducts classical Lie symmetry analysis and derives new group invariant solutions examining both general and specific cases of the American put option under the CEV model. Recent literature on the CEV model and its applications in mathematical finance can be found in [31,4,12,25,18,21].…”

mentioning

confidence: 99%

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

Javaid,

Aziz,

Aziz

2024

DCDS-S

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This study aims to use the classical Lie symmetry algorithm to solve a mathematical model that represents the American put option. The model is based on a constant elasticity of variance (CEV) framework and includes factors like dividend yield. An infinitesimal transformation and symmetry generators are obtained for the governing parabolic (1+1) PDE which is also known as a price equation. Classical symmetries for the Black Scholes, Cox-Ingersoll-Ross, and general CEV models with dividend yield help us understand the mathematical structure of these models and their relationships, enabling us to develop more accurate pricing models and better understand investment risks. Group invariant solutions of governing PDE are obtained by using similarity variables which are evaluated by solving the characteristic equation of the symmetry operator. A graphical representation of solutions with different dividend yields is presented and discussed to identify the new attribute. The results indicate that rising interest rates, volatility, dividends, and expiration time conform to the established trends. The effects of the dividends yield in all three cases show a high premium value.

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Lie analysis, conserved quantities and solitonic structures of Calogero-Degasperis-Fokas equation

Cited by 16 publications

References 58 publications

Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation

Resonant multi-soliton and multiple rogue wave solutions of (3+1)-dimensional Kudryashov-Sinelshchikov equation

Conserved quantities and travelling wave profiles to the nonlinear transmission line via Lie group analysis

Analyzing the American portfolio options within the CEV model incorporating dividend yield by the Lie symmetry approach

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