Tsunamis, rogue waves, lump waves, mixed lump strip solitons, rational solitons, breathers, and their interactions with kink waves

Large-scale disturbances, like earthquakes, volcanic eruptions, landslides, or glacier calving, produce tsunamis, which cause vast amounts of water to be displaced and long-wavelength waves that can get taller as they get closer to shallow waters. The study of tsunami waves took into account significant wave characteristics like width, velocity, and collision by solving the damped geophysical model analytically. First, by applying appropriate transformation and the Hirota bilinear method (HBM) to the tsunami wave model, we analyze a formal wave propagation that shows discrete lumps, breathers, and their interactions. For the governing equation, localized solutions in the form of lump solutions and multiple lump wave solutions are found via a positive quadratic transformation. The lump one strip, lump two strips, lump periodic solutions, and a variety of interactions are computed, among distinct lumps, 1-kink wave (KW), and 2-kink waves, respectively, by using a mix of positive quadratic, exponential, and trigonometric transformations. Positive quadratic transformation and cosine are combined to evaluate the rogue waves (RW) solutions. Next, the Ma-breathers (MBs), Kuznetsov-Ma breathers (KMBs), and generalized breathers (GBs) are computed together with the corresponding standard RWs. Furthermore, we use the logarithmic transformation and symbolic computation with ansatz function technique to obtain Homoclinic breathers (HBs), M-shape solitons, interaction of one kink and M-soliton, interaction of two kink and M-soliton, interaction of RW, KWs, and M-soliton. Also, the periodic cross-rational solutions (PCRs), multi-wave solutions, amplitude, energy, and solitary wave relations are obtained.