Homoclinic breather, M-shaped rational, multiwaves and their interactional solutions for fractional quadratic-cubic nonlinear Schrödinger equation

Batool, Tahira; Seadawy, Aly R.; Rizvi, Syed T. R.; Ali, Kashif

doi:10.1007/s11082-022-04280-9

Cited by 8 publications

(3 citation statements)

References 47 publications

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“…Using Equation (), multi‐waves method, homoclinic breather approach, and interactional solution with double

\mathit{\exp}

‐functions strategy are discussed [55–60].…”

Section: Cubic Law Nonlinearity and The Fractional‐order Complex Tran...mentioning

confidence: 99%

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

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This work concerns the fractional‐order dual‐mode nonlinear Schrödinger equation (FDMNLSE), which portrays the augmentation or absorption of dual waves. This model dissects the concurrent generation of two characteristic waves dealing with dual modes and introduces three physical parameters: nonlinearity, phase velocity, and dispersive factor. In the context of photonics, NLSE models the propagation of soliton pulses over intercontinental distances. Throughout this work, the fractional derivative is given in terms of time and space conformable sense. We analyze the multi‐waves method, homoclinic breather approach, and interactional solution with the double ‐functions procedure, and their applications for this equation are obtained using logarithmic transformation. The multi‐wave method is a well‐known phenomenon in nonlinear science that describes the interaction of three waves that satisfy certain resonance conditions. A breather wave is a localized and oscillatory solution that maintains its shape over time. Finally, we will discuss the dynamics of our newly obtained solutions with the help of graphs by assigning appropriate values to the parameters. The proposed methods are straight and aggressive, so the approved form can be extended for more nonlinear models. The findings are exceptional in comparison to previous findings in the literature. These outcomes may have significance for additional investigation of such frameworks to handle the nonlinear issues in applied sciences. The obtained results help us understand fluid propagation and incompressible fluids.

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“…Using Equation (), multi‐waves method, homoclinic breather approach, and interactional solution with double

\mathit{\exp}

‐functions strategy are discussed [55–60].…”

Section: Cubic Law Nonlinearity and The Fractional‐order Complex Tran...mentioning

confidence: 99%

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Kopçasız,

Yaşar

2023

Math Methods in App Sciences

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“…Analyzing traveling wave solutions, especially for non-linear coupled systems and higher-order NLEEs [44], provides valuable insights into the underlying physical phenomena. Lately, several systematic and potent methods have been developed to derive wave solutions of NLEEs such as modified extended algebraic method [45,46], double (G 0 /G, 1/G)-exponential technique [47], positive quadratic technique [48] and so on [49,50]. The investigation of solutions, structures and interactions has garnered substantial attention, resulting in diverse and meaningful outcomes [51][52][53][54].…”

Section: Introductionmentioning

confidence: 99%

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

Arshad,

Aldosary,

Batool

et al. 2024

PLoS ONE

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This paper aims to extend the applications of the projected fractional improved Adomian Decomposition method (fIADM) to the fractional order new coupled Korteweg-de Vries (cKdV) system. This technique is significantly recognized for its effectiveness in addressing nonlinearities and iteratively handling fractional derivatives. The approximate solutions of the fractional-order new cKdV system are obtained by employing the improved ADM in fractional form. These solutions play a crucial role in designing and optimizing systems in engineering applications where accurate modeling of wave phenomena is essential, including fluid dynamics, plasma physics, nonlinear optics, and other mathematical physics domains. The fractional order new cKdV system, integrating fractional calculus, enhances accuracy in modeling wave interactions compared to the classical cKdV system. Comparison with exact solutions demonstrates the high accuracy and ease of application of the projected method. This proposed technique proves influential in resolving fractional coupled systems encountered in various fields, including engineering and physics. Numerical results obtained using Mathematica software further verify and demonstrate its efficacy.

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“…Solitons include acoustic solitons, electrical solitons, and optical solitons [16,5]. In general, SW are created by solving a nonlinear partial differential equation, which may be thought of as both a nonlinear behavior of matter and a solution of nonlinear partial differential equations [8]. Loss and dispersion are the two most significant issues in optical fiber transmission.…”

Section: Introductionmentioning

confidence: 99%

Dynamical Discussion and Diverse Soliton Solutions via Complete Discrimination System Approach Along with Bifurcation Analysis for the Third Order NLSE

Rizvi,

Seadawy,

Mustafa

2023

MJMS

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The purpose of this study is to introduce the wave structures and dynamical features of the third-order nonlinear Schr\"{o}dinger equations (TONLSE). We take the original equation and, using the traveling wave transformation, convert it into the appropriate traveling wave system, from which we create a conserved quantity known as the Hamiltonian. The Jacobian elliptic function solution (JEF), the hyperbolic function solution, and the trigonometric function solution are just a few of the optical soliton solutions to the equation that may be found using the complete discrimination system (CDS) of polynomial method (CDSPM) and also transfer the JEF into solitary wave (SW) soltions. It also includes certain dynamic results, such as bifurcation points and critical conditions for solutions, that might be utilized to explore the dynamic features of the equation employing the CDSPM. This method could also be used for qualitative analysis. The qualitative analysis is used to illustrate the equilibrium points and phase potraits of the equation. Phase portraits are visual representations used in dynamical systems to illustrate a system's behaviour through time. They can provide crucial information about a system's stability, periodic behaviour, and the presence of attractors or repellents.

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Homoclinic breather, M-shaped rational, multiwaves and their interactional solutions for fractional quadratic-cubic nonlinear Schrödinger equation

Cited by 8 publications

References 47 publications

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Exploration of interactional phenomena and multi‐wave solutions of the fractional‐order dual‐mode nonlinear Schrödinger equation

Exploring fractional-order new coupled Korteweg-de Vries system via improved Adomian decomposition method

Dynamical Discussion and Diverse Soliton Solutions via Complete Discrimination System Approach Along with Bifurcation Analysis for the Third Order NLSE

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