Nonlinear wave interaction problems in three dimensional case

TL;DR

This paper analytically describes three-dimensional nonlinear wave interactions, demonstrating that waves behave like simple waves and distort after collision, with the distortion quantifiable.

Contribution

It introduces an analytical method for studying 3D nonlinear wave interactions in quasilinear systems with semi-Hamiltonian reductions, highlighting wave behavior and distortion.

Findings

Waves behave like simple waves during interaction

Wave distortion after collision can be analytically calculated

Interaction studied in the context of semi-Hamiltonian systems

Abstract

Three dimensional nonlinear wave interactions have been analytically described. The procedure under interest can be applied to three dimensional quasilinear systems of first order, whose hydrodynamic reductions are homogeneous semi-Hamiltonian hydrodynamic type systems (i.e. possess a diagonal form and infinitely many conservation laws). The interaction of N waves was studied. In particular we prove that they behave like simple waves and they distort after the collision region. The amount of the distortion can be analytically computed.