Modulated positron-acoustic waves and rogue waves in a magnetized plasma system with nonthermal electrons and positrons

Mouhammadoul, B. B.; Alim,; Tiofack, C. G. L.; Mohamadou, Alidou

doi:10.1007/s10509-020-03805-6

Cited by 4 publications

(2 citation statements)

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“…The nonlinear Schrödinger equation (NLSE) is a fundamental equation in nonlinear optics, quantum mechanics and the physics of plasma, describing the dynamics of modulated wave propagation in nonlinear media. It is a partial DE incorporating dispersion and nonlinear effects, allowing for the study of nonlinear phenomena such as modulated envelope solitons, rogue waves and breathers, as well as the study of the modulational instability of modulated nonlinear wave [20][21][22][23][24][25]. The NLSE can be derived from the linear Schrödinger equation by including a nonlinear term that accounts for the interaction between the wave and the medium.…”

Section: Introductionmentioning

confidence: 99%

“…Solitons are particularly interesting due to their robustness and potential applications in high-speed communication systems. The NLSE exhibits various solutions, ranging from simple plane waves to complex localized structures such as bright solitons, dark solitons, rogue waves and breathers [20][21][22][23][24][25]. These solutions arise due to the delicate balance between dispersion, which tends to be associated with wave propagation, and nonlinearity, which counteracts the spreading by self-focusing or self-defocusing effects.…”

Section: Introductionmentioning

confidence: 99%

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On the Solitary Waves and Nonlinear Oscillations to the Fractional Schrödinger–KdV Equation in the Framework of the Caputo Operator

Noor,

Alotaibi,

Shah

et al. 2023

Symmetry

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The fractional Schrödinger–Korteweg-de Vries (S-KdV) equation is an important mathematical model that incorporates the nonlinear dynamics of the KdV equation with the quantum mechanical effects described by the Schrödinger equation. Motivated by the several applications of the mentioned evolution equation, in this investigation, the Laplace residual power series method (LRPSM) is employed to analyze the fractional S-KdV equation in the framework of the Caputo operator. By incorporating both the Caputo operator and fractional derivatives into the mentioned evolution equation, we can account for memory effects and non-local behavior. The LRPSM is a powerful analytical technique for the solution of fractional differential equations and therefore it is adapted in our current study. In this study, we prove that the combination of the residual power series expansion with the Laplace transform yields precise and efficient solutions. Moreover, we investigate the behavior and properties of the (un)symmetric solutions to the fractional S-KdV equation using extensive numerical simulations and by considering various fractional orders and initial fractional values. The results contribute to the greater comprehension of the interplay between quantum mechanics and nonlinear dynamics in fractional systems and shed light on wave phenomena and symmetry soliton solutions in such equations. In addition, the proposed method successfully solves fractional differential equations with the Caputo operator, providing a valuable computational instrument for the analysis of complex physical systems. Moreover, the obtained results can describe many of the mysteries associated with the mechanism of nonlinear wave propagation in plasma physics.

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