Characterizing the physical and dynamical properties of lump, rogue waves and their interactions for a cascaded system with spatio-temporal dispersion and Kerr nonlinearity

This article uses Hirota's bilinear method (HBM) and appropriate transformations to investigate several lump solution forms in a cascaded system with spatiotemporal dispersion (STD) and Kerr law nonlinearity (KLN). The vector-coupled nonlinear Schrödinger equation is the mathematical model that describes how different solitons propagate through a cascaded system. Using the positive quadratic assumption in bilinear form, we evaluate lump solutions. By using the single and double exponential ansatz in bilinear form, respectively, we additionally investigate lump single-strip and double-strip soliton interactions. Furthermore, by using trigonometric and hyperbolic functions, respectively, we are able to find lump periodic and rogue wave solutions. Additionally, we discuss and illustrate the geometry of our solutions in multiple dimensions, such as contour plots and 3D. We also compute the stability of our solutions.