Lie symmetry analysis and conservation laws with soliton solutions to a nonlinear model related to chains of atoms

Rizvi, Syed T. R.; Seadawy, Aly R.; Bashir, Azhar; Nimra,

doi:10.1007/s11082-023-05049-4

Cited by 7 publications

(1 citation statement)

References 38 publications

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“…Nonlinear partial differential equations (NPDEs) are extensively employed to portray a diverse array of dynamic phenomena in engineering and the applied sciences [1][2][3]. The development of nonlinear evolution equations is imperative for attaining a profound understanding of complex natural phenomena across various disciplines such as physics, applied mathematics, and engineering [4][5][6]. Among the plethora of partial differential equations, the Schrödinger equation stands out as a pivotal formulation, playing a fundamental role in quantum mechanics [7,8].…”

Section: Introductionmentioning

confidence: 99%

Various exact solutions to the time-fractional nonlinear Schrödinger equation via the new modified Sardar sub-equation method

Murad,

Ismael,

Sulaiman

2024

Phys. Scr.

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We aim to investigates the nonlinear Schrödinger equation including time-fractional derivative in (3+1)-dimensions by considering cubic and quantic terms. The modified Sardar sub-equation method is used that lead to the discovery of a unique class of optical solutions. To transform the suggested nonlinear equation into an ordinary differential equation, we applied wave transformations, resulting in a set of nonlinear equations that offer diverse solution scenarios. The derived solutions encompass dark, wave, bright, mixed dark-bright, bell-shape, kink-shape, and singular soliton solutions. To enhance our understanding of the dynamic behavior exhibited by these solitons under varying time parameter values, visual simulations through a variety of graphs is presented. Furthermore, a comprehensive comparison is conducted, exploring a range of values for the conformable fractional order parameter. This comparison aims to highlight on the influence of fractional order variations on the solutions, contributing valuable insights into the nuanced dynamics of the system. Overall, this study serves to advance our understanding of nonlinear processes, and its potential applications in real-life phenomena. In the field of nonlinear optics, this equationcan describe the propagation of optical pulses in nonlinear media. It helpsin understanding the behavior of intense laser beams as they propagatethrough materials exhibiting nonlinear optical effects such as self-focusing,self-phase modulation, and optical solitons.

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