Numerical simulations of the soliton dynamics for a nonlinear biological model: Modulation instability analysis

Vivas-Cortez, Miguel; Arshed, Saima; Sadaf, Maasoomah; Perveen, Zahida; Akram, Ghazala

doi:10.1371/journal.pone.0281318

Cited by 9 publications

(1 citation statement)

References 30 publications

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“…Analytical solutions for non-linear evolution equations (NLEEs) play a crucial role in understanding nonlinear problems across various applied sciences [1][2][3][4]. The pursuit of analytical solutions for diverse NLEEs is essential, and recent literature reflects a notable effort to obtain traveling wave solutions [5][6][7][8], typically relying on variables associated with traveling waves [9,10].…”

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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