The Effect of <i>q</i> ‐Nonextensive Distribution on Breather Structures in Dusty Plasma With Generalized Polarization Force

ABSTRACT This theoretical study investigates the nonextensive effect on breather structures in dusty plasma with modified polarization force. The plasma model comprises positively and negatively charged dust grains, along with ions and electrons. We examine breather soliton structures by deriving 1‐soliton and 2‐soliton solutions within the framework of the Gardner Equation (GE), in an inhomogeneous, unmagnetized dusty plasma affected by a generalized polarization force. The nonlinear evolution equation, that is, the GE, which extends the Korteweg–de Vries (KdV) equation by incorporating both quadratic and cubic nonlinearities, is obtained using the Reductive Perturbation Technique (RPT). The breather solutions are derived by applying the Hirota Bilinear Method (HBM) to the GE. Our findings reveal that the q ‐nonextensive properties of the electron and ion populations significantly impact the characteristics of breather solitons. Such oscillatory wave packets are known to play important roles in hydrodynamics and nonlinear optics, where their interactions can alter the dynamics of the surrounding wave field. The insights gained from this study may also have applications in understanding finite‐amplitude wave propagation in natural environments such as the atmosphere, oceans, optical fibers, and signal processing systems.