Symmetry analysis,closed-form invariant solutions and dynamical wave structures of the generalized (3+1)-dimensional breaking soliton equation using optimal system of Lie subalgebra

Nonlinear evolution equations(NLEEs)are primarily relevant to nonlinear complex physical systems in a wide range of fields,including ocean physics,plasma physics,chemical physics,optical fibers,fluid dy-namics,biology physics,solid-state physics,and marine engineering.This paper investigates the Lie sym-metry analysis of a generalized(3+1)-dimensional breaking soliton equation depending on five nonzero real parameters.We derive the Lie infinitesimal generators,one-dimensional optimal system,and geo-metric vector fields via the Lie symmetry technique.First,using the three stages of symmetry reductions,we converted the generalized breaking soliton(GBS)equation into various nonlinear ordinary differential equations(NLODEs),which have the advantage of yielding a large number of exact closed-form solu-tions.All established closed-form wave solutions include special functional parameter solutions,as well as hyperbolic trigonometric function solutions,trigonometric function solutions,dark-bright solitons,bell-shaped profiles,periodic oscillating wave profiles,combo solitons,singular solitons,wave-wave interac-tion profiles,and various dynamical wave structures,which we present for the first time in this research.Eventually,the dynamical analysis of some established solutions is revealed through three-dimensional sketches via numerical simulations.Some of the new solutions are often useful and helpful for study-ing the nonlinear wave propagation and wave-wave interactions of shallow water waves in many new high-dimensional nonlinear evolution equations.