Bifurcations and Exact Solutions of the Coupled Nonlinear Generalized Zakharov Equations with Anti-Cubic Nonlinearity: Dynamical System Approach

Jie Song, Feng Li () and Mingji Zhang ()
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Jie Song: School of Mathematics and Statistics, Linyi University, Linyi 276005, China
Feng Li: School of Mathematics and Statistics, Linyi University, Linyi 276005, China
Mingji Zhang: Department of Mathematics, New Mexico Institution of Mining and Technology, Socorro, NM 87801, USA

Mathematics, 2025, vol. 13, issue 2, 1-15

Abstract: We consider the exact traveling wave solutions for the coupled nonlinear generalized Zakharov equations. By employing the method of dynamical systems, we are able to obtain bifurcations of the phase portraits of the corresponding planar dynamical system under various parameter conditions. Based on different level curves, we derive all possible exact explicit parametric representations of bounded solutions, which include pseudo-periodic peakon, pseudo-peakon, smooth periodic wave solutions, solitary solutions, kink wave solution and the compacton solution family.

Keywords: solitary wave; periodic wave; pseudo-periodic peakon; pseudo-peakon; compacton; bifurcation; generalized Zakharov equations (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2025
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