Exploring soliton solutions and dynamical features of three dimensional Gardner Kadomtsov Petviashvili equation.

Amjad Hussain, Muhammad Zeeshan, Muhammad Junaid U Rehman, Adil Jhangeer

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Article in Scientific reports, 2025. The graph could read no effect estimate from its abstract, so it casts no vote on the map. Not yet cited in PubMed.

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4 authors.

Amjad HussainDepartment of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan. a.hussain@qau.edu.pk.

Muhammad ZeeshanDepartment of Mathematics, Quaid-i-Azam University, 45320, Islamabad, 44000, Pakistan.

Muhammad Junaid U RehmanDepartment of Automation, Biomechanics, and Mechatronics, Lodz University of Technology, 1/15 Stefanowski st., 90- 537, Łódź, Poland.

Adil JhangeerIT4Innovations, VSB-Technical University of Ostrava, Ostrava-Poruba, Czech Republic.

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6 · The paper itself

Abstract

In this paper, the dynamical features and soliton structures of the Gardner-Kadomtsov-Petviashvili equation in three dimensions are looked at. The Jacobi elliptic function method yields wave solutions that display distinct behaviors based on parameter variations. We reformulate the system into a planar dynamical system via the Galilean transformation for further analysis.Phase portraits are depicted by adjusting the bifurcation parameters , while periodic and super nonlinear periodic wave solutions are portrayed using numerical simulations. Furthermore, quasi-periodic and chaotic behavior is depicted by varying the external forcing term and using tools such as Lyapunov exponents, Poincaré maps, and sensitivity analysis. Changes in frequency and amplitude strongly influence the system's dynamics, offering insights that can improve predictions, enhance control methods, and optimize model performance.

Indexed as

(3+1)-dimensional Gardner–Kadomtsov–Petviashvili equationJacobi elliptic function methodPhase portraitsQuasi-periodic and chaotic behaviorSoliton solutions

Identifiers

PMID41131275

DOI10.1038/s41598-025-22968-2

PMCPMC12549858

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