Novel solitary wave solutions and bifurcation analysis of multispecies dusty plasma consisting of cold dust grains

Abstract

This study focuses on revealing closed-form solutions for traveling waves in the nonlinear dynamical model of dust-acoustic waves in multispecies of dusty plasma. Plasma consists of cold dust grains, along with isothermal electrons and positive ions for balance. Fluid equations simplify through reductive perturbation, yielding the modified Korteweg–de Vries equation for analyzing weak dust-acoustic solitons. Applying this method to a specific scenario involving negatively charged dust grains and protons with all electrons bound to the dust grains shows support for rarefactive supersonic solitons, contrasting with typical compressive ion-acoustic solitons. Introducing streaming reveals a subtle soliton amplitude decrease. Using the Generalized exp(-S(φ)) expansion method effectively derives various soliton solutions, including kink, anti-kink, singular, hyperbolic functions, and diverse solitary waves. Furthermore, the equation’s dynamic behaviors are explored through equilibrium point bifurcations. Employing a Galilean transformation, the model is transformed into a planar dynamical system, and qualitative inspection is performed. Phase portraits depict bifurcation outcomes. Our methodology is significant for tackling the novel problem and applying previously untested approaches in this context, resulting in the development of multiple exact and novel optical soliton solutions. This highlights the efficiency and broad application of our new strategy to addressing nonlinear challenges in astrophysics, laboratories, space, and technology.

Keywords

• Dust-acoustic waves
• Closed-form solutions
• Bifurcation analysis
• Dusty plasma