Abstract
The present study is devoted to obtaining some exact generalized solutions and new solitary wave solutions for a (2+1)-dimensional nonlinear rth dispersionless Dym (rdDym) equation by utilizing the Lie symmetry analysis. The Lie infinitesimals, geometric vector fields, the commutation relation of the symmetry Lie algebra are derived by employing the Lie group symmetry technique. Thenceforth, explicit exact closed-form solutions are achieved through two stages of symmetry reductions. These closed-form solutions include arbitrary independent functional parameters and other constant parameters, therefore exhibiting rich localized solitons and comprising the existing solutions in the literature. Furthermore, the different dynamical wave structures of established soliton solutions in the forms of oscillating periodic multisolitons, the interaction between four lump-solitons with parabolic waves, W-shaped solitons, and the interaction between two-doubly solitons with parabolic waves, periodic multi-solitons, and parabolic-shaped solitons profiles are exhibited graphically through three-dimensional plots.
•The (2+1)-dimensional nonlinear rdDym equation is investigated.•The infinitesimals, geometric vector fields, and commutation relation of Lie algebra are derived.•Some more new exact closed-form solutions of the rdDym equation are constructed.•Dynamical behavior of the established soliton solutions is analyzed via 3-D plots.•This type of study is highly recommended in the areas of research and development.