Modulation instability analysis and analytical solutions to the system of equations for the ion sound and Langmuir waves

Abstract

The core of this research is to investigate the system of equations for the ion sound and Langmuir waves through the Bernoulli sub-equation method. It is one of the most effective methods for solving nonlinear ordinary differential equations. To transform a given system to a nonlinear ordinary differential equation, a traveling wave transformation has been implemented. Novel wave behaviors of the guiding system are acquired, such as kink-type singular solutions, wave solutions, periodic wave solutions, and periodic singular solutions. Besides, the modulation instability analysis of the given system is investigated based on the standard linear stability analysis and the modulation instability gain spectrum analysis. Furthermore, 2D, 3D and contour graphs of all acquired solutions are also plotted under the selection of appropriate parameter values.