Oblique interactions between solitons and mean flows in the Kadomtsev–Petviashvili equation

The interaction of an oblique line soliton with a one-dimensional dynamic mean flow is analyzed using the Kadomtsev-Petviashvili II (KPII) equation. Building upon previous studies that examined transmission or trapping by slowly varying rarefaction oscillatory dispersive shock wave in one space and time dimension, this paper allows for incident to approach changing at nonzero angle. By deriving invariant quantities soliton-mean modulation equations$-$a system three (1+1)-dimensional quasilinear, hyperbolic equations parameters$-$and positing initial configuration as Riemann problem variables, it possible derive quantitative predictions regarding evolution within flow. It found between leads several novel features not observed reduced problem. Many these interesting dynamics arise from unique structure are nonstrictly hyperbolic, including well-defined multivalued solution interpreted (2+1)-dimensional equations, which interacts then wraps around interact again. Finally, shown interactions solitons solutions give rise all types 2-soliton KPII analytical findings quantitatively supported direct numerical simulations.