https://doi.org/10.1140/epjp/s13360-023-04803-7
Regular Article
Nonlinear gradient term effects on the stability of localized structures in parametrically forced extended dissipative systems
Pure Physics Laboratory, Group of Nonlinear Physics and Complex Systems, Department of Physics, Faculty of Science, University of Douala, P.O. Box 24157, Douala, Cameroon
Received:
5
July
2023
Accepted:
16
December
2023
Published online:
2
January
2024
We study the influence of the nonlinear gradient term on the localized solutions generated by a parametrically forced complex Ginzburg Landau equation (FCGLE) with a forcing frequency equal to half that of the oscillations. We use the weakly linear theory and consider the weaks damping and forcing cases to find an analytical solution which decreases in the presence of the nonlinear gradient term. The results of the numerical study confirmed that the presence of the nonlinear gradient term decreases considerably the amplitude of solutions and for certain values of these coefficients, it leads to the stabilization of the solutions which were unstable. Furthermore, we also show that the presence of the nonlinear gradient term leads to the fast convergence of the energy function. Consequently, this supports the stabilizing effect highlighted by the nonlinear gradient term.
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