Collisions of Burgers Bores with Nonlinear Waves

TL;DR

This paper explores the interaction of nonlinear waves modeled as Burgers bores overtaking solutions of KdV and NLS equations, analyzing the resulting wave states and introducing stochastic modeling via SALT.

Contribution

It provides a novel analysis of overtaking collisions between Burgers bores and nonlinear waves, including stochastic modeling of the system.

Findings

Wave state depends on nonlinearity-dispersion balance

Numerical simulations reveal qualitative differences in wave interactions

Stochastic modeling extends analysis to uncertain environments

Abstract

This paper treats nonlinear wave current interactions in their simplest form, as an overtaking collision. In one spatial dimension, the paper investigates the collision interaction formulated as an initial value problem of a Burgers bore overtaking solutions of two types of nonlinear wave equations, Korteweg de Vries (KdV) and nonlinear Schrodinger (NLS). The bore wave state arising after the overtaking Burgers-KdV collision in numerical simulations is found to depend qualitatively on the balance between nonlinearity and dispersion in the KdV equation. The Burgers-KdV system is also made stochastic by following the stochastic advection by Lie transport approach (SALT).