Langmuir waves trapping in a (1+2) dimensional plasma system. Spectral and modulation stability analysis

Abstract

A variety of works on the (1+1) dimensional system of ion sound and Langmuir waves were carried in the literature. A novel transformation, which is based on considering complex amplitude, is introduced. The effects of soliton periodic wave elastic or inelastic interactions are inspected via this transformation. In the present work, we are concerned with investigating the behavior of waves configuration via traveling waves solutions of the (2+1) dimensional system. These solutions are obtained by using the unified method. Numerical evaluations are carried and the solutions are represented in graphs. Multiple waves structures are exhibited. Among them, longitudinal and transverse waves with quasi-tunneling. That reveals a relevant physical phenomena, which is Langmuir wave trapping in the depletion. It may be due to the ponderomotive force produced by a pressure field. This novel phenomena was not remarked in the (1+1) dimensional system. Thus, this result is new. It is also remarked that in the regions of quasi-tunneling the density varies significantly. The characteristics of the electric field are identified and analyzed. Further, the modulation instability is studied, where it is established that it occurs when the electric field dispersion coefficient (α) exceeds a critical value. We think that it leads to the wave trapping. This result agrees with what was found in the literature, that is when the modulational instability threshold exceeds its critical value, irregularity in the wave–wave interactions occurs. Furthermore, the characteristics of waves, wave number, frequency and spectrum are illustrated. The calculations are carried via symbolic computations via Mathematica 12.