https://doi.org/10.1140/epjp/s13360-026-07557-0
Regular Article
Nonlinear pulsational modes in 
-deformed spherical tripolar dust molecular clouds to structure formation
1
Department of Physics, Tezpur University, 784028, Napaam, Sonitpur, Assam, India
2
Department of Physics, Faculty of Science, Alexandria University, 21511, Alexandria, Egypt
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Received:
4
December
2025
Accepted:
9
March
2026
Published online:
20
April
2026
Abstract
The astrophysical mechanism responsible for hierarchical bounded structure formation in diverse cosmic environments has been an active research frontier for decades. In particular, gravitational collapse dynamics in dust molecular clouds (DMCs) plays a central role in star formation processes. In this context, nonlinear analyses incorporating the presence of negative ions and tripolar dust still remain unexplored. We herein develop a theoretical model formalism to study the nonlinear pulsational mode of gravitational collapse (PMGC) dynamics in spherically symmetric astrophysical DMCs. The macroscopic DMC state is presumed to exist in a globally quasi-neutral, hydrostatic, and homogeneous equilibrium. It comprises lighter nonthermal species, such as electrons, positive ions, and negative ions, modeled with the -deformed Kaniadakis distribution laws, with heavier dust grains as viscous fluids. The dust thermodynamics is described amid the Larson logatropic barotropic equation of state. Applying the nonlinear Wentzel, Kramers, Brillouin (WKB) perturbation method, we methodically derive a pair of gravitoelectrostatically coupled extended Korteweg-de-Vries (ce-KdV) equations. Numerical analysis reveals the excitation of a conjugational pair-hybrid solitary wave train modal pattern, alongside their diverse multiparametric stability properties. This study further shows that the PMGC dynamics exhibits non-conservative behaviors due to the collective dust-induced coupling effects. This ce-KdV study offers essential insights into the self-gravitational collapse phenomena relevant to early-stage star formation scenarios.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2026
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
