Abstract
Applying several latest theoretical techniques, the empirical description of the interaction between the high-frequency Langmuir and the low-frequent ion-acoustic waves, derived mathematically by Zakharov’s non-dimensional (ZE) equation. These interactions are described in electromagnetic waves, plasma physics, signal processing through optical fibers, coastal engineering, and fluid dynamics. Three modern computing methods are being used to construct several solutions: the extended exp(ϕ)-expansion process,the popular Kudryashov process, and the modified Khather method. Centered on the properties of the Hamilton system, the stability properties of the solutions are investigated. The physical proprieties are illustrated using 3D plots. The originality of the obtained solutions is explored. We demonstrate that we retrieve the old known solutions and we obtain new solutions that have never been found before.
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