Interaction of Inward and Outward Cylindrical and Spherical Solitary Rings in Quantum Electron Ion Dust Plasmas

Wave–wave interaction, specifically solitary ring interaction in nonplanar geometry is an important source of information to study the nature and the characteristics of cylindrical and spherical solitary waves structures. A theoretical investigation by an all-inclusive adaptation of the Poincare–Lighthill–Kuo (PLK) technique is carried out to study the inward and outward interaction between two cylindrical and spherical dust–ion–acoustic cylindrical and spherical solitary rings in electron–ion dust quantum plasma. The interactions and collisions between two cylindrical and spherical geometries at different times are depicted. Also, the combined effects of the quantum diffraction parameters H e , H i , and the geometric configuration have been studied in detail on the phase shifts raised due to collision. The crucial role of quantum diffraction parameters H e , H i , and the geometric configuration parameter upon the derived phase shift have been studied. It has been observed that the properties of the interaction of dust–ion–acoustic solitary rings in cylindrical and spherical geometry are distinct.