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Chaos in Plasma Physics
Published in Christos H. Skiadas, Charilaos Skiadas, Handbook of Applications of Chaos Theory, 2017
Dan-Gheorghe Dimitriu, Maricel Agop
The transition indicated in Figure 19.5, from the frequency f1 to f2, proves that the moving DL dissolves and sustains ion-acoustic-like oscillations in the background plasma. The fundamental frequency of these oscillations (~14kHz) is small compared to the ion plasma frequency; so, the dispersion relation of the ion-acoustic wave is linear. The ion-acoustic waves are compressive spherical ones [93], which are usually proved by measuring the electronic saturation current of the probe during one period of the ion-acoustic instability and also by localized measurements of the ion density where the DL dissolves [9].
Construction of analytical wave solutions to the conformable fractional dynamical system of ion sound and Langmuir waves
Published in Waves in Random and Complex Media, 2022
U. Younas, Aly R. Seadawy, M. Younis, S.T.R. Rizvi
Ion acoustic waves are kind of longitudinal oscillation of ions and electrons, which are very similar to acoustic waves and are also considered as sound waves in a plasma. Acoustic waves spread by ways of adiabatic pressure and decompression, where as longitudinal waves have the same vibrational direction in their traveling direction. It is because these waves are propagated through positively charged ions and ion acoustic waves are interacted with EMF along with simple collisions. Plasma oscillations, also known as Langmuir waves (in the wake of Irving Langmuir), are rapid electron density oscillations in ultraviolet conductive material, such as plasmas or metals. The oscillations in the di-electrical function of a free electron gas can be defined as instability. The frequency is only weakly dependent on the oscillation wavelength. The quasi particle resulting from the quantization of these oscillations is the plasmon. American physicists Irving Langmuir and Lewi Tonks in the 1920s discovered the Langmuir waves.
Novel methods for finding general forms of new multi-soliton solutions to (1+1)-dimensional KdV equation and (2+1)-dimensional Kadomtsev–Petviashvili (KP) equation
Published in Waves in Random and Complex Media, 2019
It is worth to mention that the investigation of multi-soliton solutions of NLEEs will help one to understand these phenomena better. We have presented the investigation of ion-acoustic waves and structures in plasma in our latest work [40]. After applying the model 2 to deal the (2+1)-dimensional Zakharov–Kuznetsov (ZK) equation, the electric field potential of ZK equation are formally obtained, which are presented as the multi-soliton solutions. And the propagation structures of multi-soliton are elaborated. Meanwhile, the electric field and magnetic field can be accordingly obtained. In addition, the significant features of the variable coefficient and the electron temperature parameter are discovered.
The singular manifold method for a class of fractional-order diffusion equations
Published in Waves in Random and Complex Media, 2021
R. Saleh, Samah M. Mabrouk, Abdul Majid Wazwaz
Some solutions are graphically represented in 3D plots, revealing different solitary wave solutions. The resulting solutions help study ion-acoustic waves in plasma applications and nonlinear optics. The technique used in this work is new and effective in studying FPDEs compared with the other methods in recent research. The SMM is useful for obtaining closed-form solutions of fractional-order differential equations and partial differential equations and can be extended to discuss and analyze more complicated fractional-order NLPDEs. The obtained results are new and will be helpful for anyone working in a related field.