Lie vector fields, conservation laws, bifurcation analysis, and Jacobi elliptic solutions to the Zakharov–Kuznetsov modified equal-width equation

Hosseini, K.; Alizadeh, F.; Sadri, K.; Hinçal, E.; Akbulut, A.; Alshehri, H. M.; Osman, M. S.

doi:10.1007/s11082-023-06086-9

Cited by 17 publications

(1 citation statement)

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“…Substantial investigations have previously explored the behavior of solitons, utilizing various nonlinear frameworks like the Sakovich equation [13], Schrödinger equation [14], and Zakharov-Kuznetsov modified equal-width equation [15]. The integrable equations in (3 + 1) dimensions have been the subject of increased research attention lately.…”

Section: Introductionmentioning

confidence: 99%

Analyzing Dynamics: Lie Symmetry Approach to Bifurcation, Chaos, Multistability, and Solitons in Extended (3 + 1)-Dimensional Wave Equation

Riaz,

Jhangeer,

Duraihem

et al. 2024

Symmetry

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The examination of new (3 + 1)-dimensional wave equations is undertaken in this study. Initially, the identification of the Lie symmetries of the model is carried out through the utilization of the Lie symmetry approach. The commutator and adjoint table of the symmetries are presented. Subsequently, the model under discussion is transformed into an ordinary differential equation using these symmetries. The construction of several bright, kink, and dark solitons for the suggested equation is then achieved through the utilization of the new auxiliary equation method. Subsequently, an analysis of the dynamical nature of the model is conducted, encompassing various angles such as bifurcation, chaos, and sensitivity. Bifurcation occurs at critical points within a dynamical system, accompanied by the application of an outward force, which unveils the emergence of chaotic phenomena. Two-dimensional plots, time plots, multistability, and Lyapunov exponents are presented to illustrate these chaotic behaviors. Furthermore, the sensitivity of the investigated model is executed utilizing the Runge–Kutta method. This analysis confirms that the stability of the solution is minimally affected by small changes in initial conditions. The attained outcomes show the effectiveness of the presented methods in evaluating solitons of multiple nonlinear models.

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Section: Introductionmentioning

confidence: 99%