A special phenomenon of wave interactions: An application of nonlinear evolution equation in (3+1)-dimension

Abstract

The Lie group transformation approach can be used in the reduction of the generalized (3+1)-dimensional nonlinear evolution equation to ordinary differential equations (ODEs). In this work, infinitesimal generators, commutator table of Lie algebra, adjoint representation of subalgebras, symmetry group, and similarity reduction for (3+1)-dimensional shallow-water-like (gSWL) equation are obtained. Interactions of soliton solutions of a gSWL equation are evaluated that depict how near-inertial waves affect the dynamics of barotropic and baroclinic balanced flows. It is shown that the temporo-spatial localization of multi-soliton complexes (MSCs), gradually escalating incoherent interactivity amidst multi parameter group of MSCs along with spatial inhomogeneity alter the shape of quasi-periodic MSCs. The interactions among bright and dark solitons are shown. The increased number of solitons and increased self-interactions among solitary waves contribute to an unstable wave field. Breathers have a well-separating and initial localized energy domain. A limiting case of breather solutions is the peregrine soliton. Thus, interactions among these soliton structures show that multiple breathers retain their wave characteristic.