https://doi.org/10.1140/epjp/s13360-023-04689-5
Regular Article
Analysis of nonlinear dynamics of Novikov–Veselov equation using solitonic solutions, bifurcation, periodic and quasi-periodic solutions, and Poincaré section
1
Department of Mathematics, University of the Punjab, Lahore, Pakistan
2
Department of Mathematics, Namal University, 30KM Talagang Road, 42250, Mianwali, Pakistan
Received:
19
June
2023
Accepted:
12
November
2023
Published online:
6
December
2023
This paper demonstrates the efficacy of the extended direct algebraic approach in generating solutions for traveling and solitary waves from higher-order nonlinear evolution equations, specifically utilizing the Novikov–Veselov equation. Kink soliton, bright and kink behaviour and singular soliton solutions have been produced by choosing specific values of the involved parameters. Hyperbolic, trigonometric and rational results have also been obtained throughout the study. All of these solutions, along with underlying assumptions, have been made accessible using suitable physical variables in 3D and 2D plots. The planar dynamical framework of the aforementioned equation has been generated through Galilean transformation. The Runge–Kutta fourth-order method has been used to extract the nonlinear periodic waves of the problem, and the outcomes have been presented using various representations. Chaotic and quasiperiodic behaviours have been observed for specific values of the examined system’s characteristics, while keeping the force and frequency of the perturbed dynamical structure constant. Sensitivity and multistability analysis have been employed to further investigate the periodic and quasiperiodic behaviours under different initial conditions. The concluding remarks of the article have been provided at the end.
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© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2023. 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.
