Optical solitons of nonlinear complex Ginzburg–Landau equation via two modified expansion schemes

Zafar, Asim; Shakeel, Muhammad; Ali, Asif; Akinyemi, Lanre; Rezazadeh, Hadi

doi:10.1007/s11082-021-03393-x

Cited by 95 publications

(14 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…At the moment, it is very beneficial to apply various techniques to solve partial differential equations (NLEEs) and nonlinear evolution equations (NLEs) in order to obtain precise solutions. One effective scheme is the Φ 6 -expansion approach [15][16][17], the Hirota bilinear method [18], the new Kudryashov approach [19], a new auxiliary equation approach [20], a sinh-Gordon equation technique [21], modified Exponential function and the Kudryshov techniques [22,23], a generalized Riccati mapping equation scheme and the q-HATM methods [24]. The Khater II approach and Sardar Sub-equation scheme [25] and utilizing conformable fractional derivative [26], a auto-Backlund transformation technique [27], the Jacobi elliptic function technique [28], the Jacobi elliptic function expansion (JEFE) method [29], the modified exponential rational functional method [30], the retrieval process utilizes the undetermined coefficients method as its integration technique [31] and so on.…”

Section: Introductionmentioning

confidence: 99%

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

Faridi,

Tipu,

Myrzakulova

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

This study investigates the Kairat-II equation, describing optical pulse behavior in opticalfibers and plasma. To uncover new solitary wave profiles, the study employs an extendeddirect algebraic method. Prior to this study, no previous research has achieved solutions ofthis kind. This innovative approach efficiently encompasses a comprehensive set of thirty-sevensolitonic wave profiles, spanning various soliton families. The investigation unveils novel solitonicwave patterns, including plane solutions, hyper-geometric solutions, mixed hyperbolic solutions,periodic and mixed periodic solutions, mixed trigonometric solutions, trigonometric solutions,shock solutions, mixed shock singular solutions, mixed singular solutions, complex solitary shock solutions, singular solutions, and shock wave solutions. To demonstrate the pulse propagationcharacteristics, the research presents 2-D, 3-D, and contour graphics based on parameter values,aiding in a better understanding of the phenomenon.

show abstract

Section: Introductionmentioning

confidence: 99%

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

Faridi,

Tipu,

Myrzakulova

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…There are multiple approaches andschemessuch as the sine-Gordon expansion scheme [26], the Kudryashov method [27], the simply extended equation method [28] and the bilinear neural network technique [29],…”

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

“…The use of various mathematical tools has led to the discovery of diverse exact solutions of NLEEs, which find application in fields such as organic chemistry, biology, fluid mechanics, population dynamics, space technology, hydrodynamics, engineering methodology, theory of Bose-Einstein condensates, computer engineering, solid-state physics and applied mathematics. Numerous solitary wave solutions have been discovered for nonlinear partial differential equations, especially in fields related to physics, including nonlinear optics, plasma theory and fluid mechanics [1][2][3][4][5][6].…”

Section: Introductionmentioning

confidence: 99%

Novel Optical bi-directional solutions to the new dual-mode derivative nonlinear Schrödinger equation

Alam,

Javid

2023

Phys. Scr.

View full text Add to dashboard Cite

In recent times, a novel category of nonlinear physical models known as dual-mode nonlinear equations has emerged. These equations include various real-valued dual-mode equations linked to widely-known single-mode equations like KdV, mKdV, Schrödinger and Burger's. Extensive research has been conducted to establish and investigate these equations. This study presents a novel dual-mode derivative nonlinear Schrödinger equation that incorporates new parameters for dissipative effects, nonlinearity, and interaction phase velocity. Various methods such as the tanh-coth scheme, extended exponential method, Kudryashov-scheme, and the sine-cosine function methods are employed to investigate the solutions of the model. The obtained solutions are illustrated through graphical 2D and 3D and to demonstrate their dynamics and shapes. Furthermore, the interaction of the dual-waves is correlated with changes in the phase-velocity parameter. This model describes propagation of two simultaneously directional waves instead of as in standard Schrödinger equation. For the propagation of solitons in nonlinear optics, the solutions found in this study have important significance. All the resulting solutions can help to comprehend the underlying mechanisms for numerous nonlinear phenomena in diverse domains, including nonlinear optics, plasma physics, Bose-Einstein condensates and others.

show abstract

Optical solitons of nonlinear complex Ginzburg–Landau equation via two modified expansion schemes

Cited by 95 publications

References 41 publications

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

The sensitivity demonstration and propagation of hyper-geometric soliton waves in plasma physics of Kairat-II equation

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

Novel Optical bi-directional solutions to the new dual-mode derivative nonlinear Schrödinger equation

Contact Info

Product

Resources

About