Drag force in bimodal cubic-quintic nonlinear Schr\"odinger equation

TL;DR

This paper investigates the drag force experienced by a probe in a two-dimensional coupled cubic-quintic nonlinear Schr"odinger system, revealing conditions for zero and non-zero drag and analyzing their dynamics through numerical simulations.

Contribution

It provides the first detailed analysis of drag forces in a coupled bimodal nonlinear Schr"odinger system, including static and traveling solutions and their dynamical behavior.

Findings

Realization of D'Alembert's paradox at small velocities

Identification of non-trivial drag forces at larger velocities

Numerical solutions for static and traveling wave configurations

Abstract

We consider a system of two cubic-quintic non-linear Schr\"odinger equations in two dimensions, coupled by repulsive cubic terms. We analyse situations in which a probe lump of one of the modes is surrounded by a fluid of the other one and analyse their interaction. We find a realization of D'Alembert's paradox for small velocities and non-trivial drag forces for larger ones. We present numerical analysis including the search of static and traveling form-preserving solutions along with simulations of the dynamical evolution in some representative examples.