https://doi.org/10.1140/epjs/s11734-026-02233-x
Regular Article
Inelastic lump–breather interactions and periodic wave dynamics in the generalized Calogero–Bogoyavlenskii–Schiff equation via a bilinear neural architecture
1
Department of Mathematics, Faculty of Science, University of Gujrat, 50700, Gujrat, Pakistan
2
Department of Mathematics and Statistics, College of Sciences, Imam Mohammad Ibn Saud Islamic University (IMSIU), Riyadh, Saudi Arabia
3
Department of Mathematical Sciences, College of Science, Princess Nourah bint Abdulrahman University, 84428, 11671, Riyadh, Saudi Arabia
a
This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
19
December
2025
Accepted:
20
February
2026
Published online:
25
March
2026
Abstract
This study presents a structured analytical framework for investigating nonlinear wave structures governed by the generalized Calogero–Bogoyavlenskii–Schiff equation, a higher-dimensional model describing multidirectional wave propagation in plasma physics, fluid systems, and optical media. The bilinear neural network method is applied as a symbolic parametrization of Hirota’s bilinear formalism, serving as an organized mechanism for generating admissible trial functions without involving any data-driven training or optimization procedure. By systematically applying coefficient balancing and symbolic computation, several classes of exact solutions are derived, including lump, three-wave interaction, breather, and periodic-type structures. The derived solutions highlight localized energy concentration, modulation dynamics, and nonlinear interaction patterns inherent to multidimensional systems. The results confirm that the proposed structured bilinear framework provides an effective and transparent approach for generating and analyzing exact solutions of higher-dimensional nonlinear evolution equations.
Copyright comment 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.
© The Author(s), under exclusive licence to EDP Sciences, 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.
