Invariance analysis, optimal system, closed-form solutions and dynamical wave structures of a (2+1)-dimensional dissipative long wave system

Abstract

By employing the one-parameter Lie group of transformations method, abundant exact invariant solutions are obtained for a (2+1)-dimensional dissipative long wave (DLW) system, which describes the water wave model of hydrodynamics with wide channels or open seas of finite depth and can also be used to illustrate nonlinear wave propagation in the dissipative medium. Initially, we derived the Lie symmetries, geometric vector fields, and commutative table, and adjoint relations of the examined vectors for the system. A one-dimensional optimal system of symmetry subalgebras is well-structured. It leads to the reduction of independent variables of the considered DLW system and leaves the system invariant. The (2+1)-dimensional DLW system is reduced into nonlinear ordinary differential equations (NLODEs) for the various subalgebras obtained through two phases of similarity reductions. Some novel closed-form solutions are obtained, including arbitrary independent functional parameters, and have never been reported in the literature. Moreover, we depict the dynamical behaviors of obtained closed-form invariant solutions like multi-wave solitons, single solitons, breather-waves, rogue waves, bell-shaped structures, Kink-waves, and Lump-waves, wave-wave interactions, and annihilation of Kink-wave profiles through three-dimensional graphics. Eventually, a comparison with other results is discussed.