Extraction of new super-Gaussian solitons via collective variables

Raza, Nauman; Hassan, Zara; Gómez-Aguilar, J. F.

doi:10.1007/s11082-021-03125-1

Cited by 18 publications

(2 citation statements)

References 25 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…used toobtain exact solitonsolutions for non-linear partial differential equations, [30] variational iteration method [31], extended exponential function method [32], Hirota bilinear technique [33], power series method [34], F-expansion technique [35] as well as several others [36][37][38][39][40][41][42].…”

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

View full text Add to dashboard Cite

In this article, the new extended direct algebraic method is used to build the exact travellingwave solutions for the non-linear time-fractional Clannish Random Walker’s Parabolic equation.This study establishes the framework in which periodic, singular, dark, bright and kink-typewave solitons are obtained with exact solutions offered by the mixed hyperbolic and trigonom-etry solutions, mixed periodic and periodic solutions, plane solutions, shock solutions, mixedtrigonometric solutions, mixed singular solutions, mixed shock single solutions, complex solitarysingular solutions, shock solutions and shock wave solutions. The exact soliton solutions of thetime-fractional clannish random walker’s parabolic equation model is graphically presented atdifferent values of involved parameters by Wolfram Mathematica software. The propagating behaviours display in 3-D, contour and 2-D surfaces of the obtained results to visualise the im-pact of the involved parameters. The sensitivity analysis is demonstrated for the wave profilesof the designed dynamical framed structure, where the soliton wave number parameter regulatesthe water wave singularity. This analysis illustrates that the utilized method is efficient andreliable and can be useful to find appropriate solutions in closed-form solitary soliton to a wide range of non-linear evolution equations. These techniques can also be utilised to find new exact travelling wave solutions for any class of integer or fractional differential equations thatarise in mathematical physics.

show abstract

Section: Introductionmentioning

confidence: 99%

Exact travelling wave solutions of time-fractional Clannish Random Walker's Parabolic equation and sensitive analysis

Asjad¹,

Ashaq²,

Faridi³

et al. 2023

Preprint

View full text Add to dashboard Cite

show abstract

“…The transmission dynamics of optical pulse in optical fiber is governed by the nonlinear Schrödinger equation (NLSE) [7,8]. In the past, analytical methods [9][10][11] were mainly used to obtain accurate solutions.…”

Section: Introductionmentioning

confidence: 99%