Novel localized waves and interaction solutions for a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions

Abstract

The Boussinesq equation has been of considerable interest in coastal and ocean engineering models for simulating surface water waves in shallow seas and harbors, tsunami wave propagation, wave overtopping, inundation, and near-shore wave process. Consequently, the study deals with the dynamics of localized waves and interaction solutions to a dimensionally reduced (2 + 1)-dimensional Boussinesq equation from N-soliton solutions by Hirota’s bilinear method. The integrability of the equation of interest was confirmed via the Painlevé test. Taking the long-wave limit approach in coordination with some constraint parameters available in the N-soliton solutions, the localized waves and interaction solutions are constructed. The interaction solutions can be obtained among the localized waves, such as (1) one breather or one lump from the two solitons, (2) one stripe and one breather, and one stripe and one lump from the three solitons, and (3) two stripes and one breather, one lump and one periodic breather, two stripes and one lump, two breathers, and two lumps from the four solitons. The interactions among the solitons are found to be elastic. The energy, phase shift, shape, period, amplitude, and propagation direction of each of the localized waves and interaction solutions are found to be influenced and controlled by the parameters involved. The dynamical characteristics of these localized waves and interaction solutions are demonstrated through some 3D and density graphs. The outcomes achieved in this study can be used to illustrate the wave interaction phenomena in shallow water.