Modeling and propagation evolution of ocean internal solitary waves

Under investigation in this article is the propagation of internal solitary waves in the deep ocean. Based on the principles of nonlinear theory, perturbation expansion and multi-scale analysis, a time-dependent modified cubic Benjamin-Ono (mCBO) equation is derived to describe internal solitary waves in the deep ocean with stronger nonlinearity. When the dispersive term vanishes, the mCBO equation transforms into the cubic BO equation. Under certain conditions, the mCBO equation can be converted to BO or modified Korteweg-de Vries (mKdV) equation. Compared with the traditional BO model, the mCBO model takes into account stronger nonlinearity. To gain deeper insights into solitary waves' characteristics, conservation of mass and momentum associated with them are discussed. By employing Hirota's bilinear method, we obtain the bilinear form and soliton solutions for mCBO equation, and subsequently investigate interactions between two solitary waves with different directions leading to the occurrence of important events such as rogue waves and Mach reflections. Additionally, we explore how certain parameters influence Mach stem while drawing meaningful conclusions. Our discoveries reveal the complex dynamics of internal solitary waves within the deep ocean and contribute to a broader understanding of nonlinear wave phenomena.