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Gross-Pitaevskii systems of fractional order with respect to multicomponent solitary wave dynamics.

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Titel: Gross-Pitaevskii systems of fractional order with respect to multicomponent solitary wave dynamics.
Autoren: Bilal, Muhammad, Alawaideh, Yazen M., Rehman, Shafqat Ur, Yousif, Majeed A., Younas, Usman, Baleanu, Dumitru, Mohammed, Pshtiwan Othman
Quelle: Scientific Reports; 7/8/2025, Vol. 15 Issue 1, p1-22, 22p
Schlagwörter: GROSS-Pitaevskii equations, FRACTIONAL calculus, RESEARCH methodology, SOLITONS, OPTICAL solitons, SUPERFLUIDITY, NONLINEAR mechanics, MATHEMATICAL models
Abstract: This study presents a comparative analysis of the fractional Gross–Pitaevskii equation (GPE), a fundamental nonlinear Schrödinger-type model, focusing on the derivation of exact soliton solutions critical for understanding nonlinear phenomena such as superfluidity and superconductivity. We compare the effectiveness of -fractional and M-truncated fractional derivatives in solving the complex fractional GPE. This comparison reveals that while both fractional derivatives enable the construction of diverse optical soliton solutions—including hyperbolic, periodic, Jacobi elliptic, and exponential forms–the -derivative provides smoother soliton profiles with computational simplicity, whereas the M-truncated derivative captures richer oscillatory dynamics due to its enhanced memory effects. Employing advanced analytical tools—namely the generalized extended direct algebraic method (gEDAM) and the Kummar-Malik (KM) method—along with Wolfram Mathematica for verification, we extract and rigorously validate a variety of exact solutions. The generated solutions and their corresponding wave profiles under varying parameters highlight the distinct physical implications of each fractional derivative approach. Our results offer a robust framework for modeling nonlinear fractional dynamics, with applications spanning optical fibers, plasma physics, mathematical physics, and condensed matter systems. The comparative insights gained deepen the understanding of fractional-order effects in nonlinear wave evolution, paving the way for further exploration in complex physical systems. [ABSTRACT FROM AUTHOR]
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Abstract:This study presents a comparative analysis of the fractional Gross–Pitaevskii equation (GPE), a fundamental nonlinear Schrödinger-type model, focusing on the derivation of exact soliton solutions critical for understanding nonlinear phenomena such as superfluidity and superconductivity. We compare the effectiveness of -fractional and M-truncated fractional derivatives in solving the complex fractional GPE. This comparison reveals that while both fractional derivatives enable the construction of diverse optical soliton solutions—including hyperbolic, periodic, Jacobi elliptic, and exponential forms–the -derivative provides smoother soliton profiles with computational simplicity, whereas the M-truncated derivative captures richer oscillatory dynamics due to its enhanced memory effects. Employing advanced analytical tools—namely the generalized extended direct algebraic method (gEDAM) and the Kummar-Malik (KM) method—along with Wolfram Mathematica for verification, we extract and rigorously validate a variety of exact solutions. The generated solutions and their corresponding wave profiles under varying parameters highlight the distinct physical implications of each fractional derivative approach. Our results offer a robust framework for modeling nonlinear fractional dynamics, with applications spanning optical fibers, plasma physics, mathematical physics, and condensed matter systems. The comparative insights gained deepen the understanding of fractional-order effects in nonlinear wave evolution, paving the way for further exploration in complex physical systems. [ABSTRACT FROM AUTHOR]
ISSN:20452322
DOI:10.1038/s41598-025-06806-z