Clout of fractional time order and magnetic coupling coefficients on the soliton and modulation instability gain in the Heisenberg ferromagnetic spin chain

Houwe, Alphonse; Abbagari, Souleymanou; Doka, Serge Y.; Bouetou, Thomas B.

doi:10.1016/j.chaos.2021.111254

Cited by 31 publications

(8 citation statements)

References 31 publications

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“…In this section, we point up the efficiency of the ALV on both MI [34][35][36] bands and the MI growth rate of the CWs by using the linearizing scheme.…”

Section: Linear Stability and Modulation Instabilitymentioning

confidence: 99%

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Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

Houwe¹,

Saliou²,

Djorwé³

et al. 2022

Phys. Scr.

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The propagation of the modulated wave pattern and its instability in the nonlinear medium is an important study from where experimental results are obtained. In this work, we use the nonlinear Schrödinger equation (NLSE) with saturation nonlinearity which describes the solitonic waves in the molecular chain model. We set our study on the eﬀectiveness of the acoustic longitudinal velocity which is related to the acoustic longitudinal vibration to investigate the behavior of the modulated wave patterns as well as the modulation instability (MI) gain. Its results are that the acoustic longitudinal velocity creates instability zones, increases MI bands, and shortens the transition regime of the modulated wave pattern. For a long time of simulation and a great enough value of the acoustic longitudinal velocity, the modulated waves feature chaos-like motion. Alongside these results the acoustic longitudinal velocity obvious itself as tool control of modulated wave as well as an energy source for the propagation of diverse modulated wave-shaped in the molecular chain.

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“…In this section, we point up the efficiency of the ALV on both MI [34][35][36] bands and the MI growth rate of the CWs by using the linearizing scheme.…”

Section: Linear Stability and Modulation Instabilitymentioning

confidence: 99%

“…The MI [34][35][36] is the event from which nonlinear and dispersion terms are used to exhibit the stable or unstable zones of the CWs in sundry media such as nonlinear OFs, plasma, and ion-acoustic just to mention these . Let's set the following with perturbed terms as the solution of the given equation (5) above…”

Section: Modulation Instabilitymentioning

confidence: 99%

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

Houwe¹,

Saliou²,

Djorwé³

et al. 2022

Phys. Scr.

Self Cite

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“…Nonlinear evolution equations (NLEEs) and their exact solutions play a substantial role in describing many nonlinear phenomena arising in physical applications. [1][2][3][4][5] The socalled positon is a fundamental solution of NLEEs on zero background, which was first proposed in the KdV equation. [6] Further, it was extended to other equations such as the Sine-Gordon equation, [7,8] the modified KdV equation, [9,10] the NLS-MB equations.…”

Section: Introductionmentioning

confidence: 99%

Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg–de Vries equations

Yuan

Ghanbari

2023

Chinese Phys. B

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Solving nonlinear partial differential equations have attracted intensive attention in the past few decades. In this paper, the Darboux transformation method has been used to derive several positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg-de Vries equations. Based on the zero seed solution, the positon solution and the hybrid solutions of positon and soliton are constructed. The composition of positons is studied which shows that multi-positons of (2+1)-dimensional equations are decomposed into multi-solitons as well as the (1+1)-dimensions. Moreover, the interactions between positon and soliton are analyzed. In addition, the hybrid solutions of b-positon and breather are obtained using the plane wave seed solution, and their evolutions with time are discussed.

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“…Fractional nonlinear evolution equations (FNLEEs), are mathematical models that describe many complicated phenomena in nature and science particularly, fiber-optic communication, transport processes, plasma physics, bio-engineering, signal processing, fluid dynamics, control theory, fractal theory, nuclear reactor kinetics, electrical circuits, and viscoelastic materials, etc [1,2]. Some noteworthy FNLLEs in the aforementioned domains are the family of Schrodinger equations [3][4][5], the Heisenberg ferromagnetic spin chain [6], Kundu-Eckhaus equation [7], the reaction-diffusion equation [8], the NPCLL equation [9], The Boussinesq equation [10], Kadomtsev-Petviashvili equation [11], The Klein-Gordon equation [12], The Zakharov-Kuznetsov (ZK) equation [13], and so on. The analytical solution of these equations piqued the interest of both theoretical and experimental researchers in the last few decades.…”

Section: Introductionmentioning

confidence: 99%

“…Based on the homogeneous balance principle of soliton theory, numerous techniques have been discovered. For instance, the Sine-Gordon expansion scheme [5], the auxiliary equation method [6], the tanh-coth method [14], the modified -expansion and modified Kudryashov methods [15], the modified -expansion function strategy [9], the Kudryashov scheme [16], the extended Kudryashov method [17], and so on. The analytical solutions derived using the methods described in the above are a sort of traveling wave solution known as a soliton solution.…”

Section: Introductionmentioning

confidence: 99%

Diverse optical soliton solutions of two space-time fractional nonlinear evolution equations by the extended kudryashov method

Devnath,

Akbar,

Gómez-Aguilar

2023

Phys. Scr.

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This study investigates the comprehensive optical soliton solutions to the (2+1)-dimensional nonlinear time-fractional Zoomeron equation and the space-time fractional nonlinear Chen-Lee-Liu equation using the extended Kudryashov technique. The newly defined beta derivative is used to conduct the fractional terms and investigate wide-spectral soliton solutions to the considered models. The general solutions yield a variety of typical soliton shapes, including V-shaped soliton, anti-bell-shaped soliton, kink soliton, periodic soliton, singular periodic soliton, etc. The three-dimensional, contour, and two-dimensional graphs of the derived solitons have been plotted to illustrate the structure, propagation, and influence of the fractional parameter. The precision of the acquired solutions is confirmed by reintroducing them into the original equation using Mathematica. The findings of this study indicate that the employed method has the capability of yielding compatible, creative, and useful solutions for diverse nonlinear evolution equations with fractional derivatives. This approach could introduce novel ways for unraveling other nonlinear equations and have implications in diverse sectors of nonlinear science and engineering.

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Clout of fractional time order and magnetic coupling coefficients on the soliton and modulation instability gain in the Heisenberg ferromagnetic spin chain

Cited by 31 publications

References 31 publications

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

Modulation instability gain and modulated wave shape incited by the acoustic longitudinal vibrations in molecular chain model

Positon and hybrid solutions for the (2+1)-dimensional complex modified Korteweg–de Vries equations

Diverse optical soliton solutions of two space-time fractional nonlinear evolution equations by the extended kudryashov method

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