Generalized (2+1)-Dimensional Sharma–Tasso–Olver–Burgers Equation: Dispersionless Decompositions and Twisted Solitons

Abstract We presents a generalized (2+1)-dimensional Sharma–Tasso–Olver–Burgers (STOB) equation, unifying dissipative and dispersive wave dynamics. By introducing an auxiliary potential y as a new space variable and employing a simpler deformation algorithm, we deform the (1+1)-dimensional STOB model to higher dimensions. The resulting equation is proven Lax-integrable via introducing strong and weak Lax pairs. Traveling wave solutions of the (2+1)-dimensional STOB equation are derived through an ordinary differential equation reduction, with implicit solutions obtained for a special case. Crucially, we demonstrate that the system admits dispersionless decompositions into two types: Case 1 yields non-traveling twisted kink and bell solitons, while Case 2 involves complex implicit functions governed by cubic-algebraic constraints. Numerical visualizations reveal novel anisotropic soliton structures, and the decomposition methodology is shown to generalize broadly to other higher dimensional dispersionless decomposition solvable integrable systems.