Soliton and its application in the study of nonlinear dynamics of acoustic waves in multi-particle fluid

Solitons have many applications in pure and applied mathematics, especially in the fields such as nonlinear differential equations, Lie algebra, and algebraic geometry. Solitons are ubiquitous in nature and have many applications in nonlinear dynamics. The discovery of solitons made it possible to obtain analytical solutions for nonlinear differential equations. Among them Korteweg-de Vries equation is the most familiar one, which is the most canonical nonlinear wave equation. In an electrostatic fluid that is partially ionized, the collision of ions with each other and also with electrons cause the propagation and coupling of ionic electrostatic waves to behave nonlinear. The equations describing the dynamics of acoustic waves in this fluid are transformed into the Korteweg-de Vries equation by the reduction perturbation method, which analytical solutions are in the form of solitary waves, and their amplitude and speed depend on the properties of the fluid medium. A brief history of solitons and their applications are given. Then, the nonlinear propagation of the traveling ion electrostatic wave in a multi-particle fluid is obtained by taking into account the production-loss rate of ions. The analytical and numerical solution of the wave equations is obtained. The results show that the wave dispersion curves have bifurcation points and only high-frequency waves are propagated as solitary waves with complex modes. The results of this study can be used in the observation of ion acoustic waves in space plasmas and the presence of dust grains in laboratory plasma.