Construction of modulated amplitude waves via averaging in collisionally inhomogeneous Bose-Einstein condensates

TL;DR

This paper uses the averaging method to analyze the existence and stability of modulated amplitude waves in collisionally inhomogeneous Bose-Einstein condensates with spatially varying scattering length, supported by numerical simulations.

Contribution

It demonstrates the existence of infinitely many modulated amplitude waves in inhomogeneous BECs using averaging, a novel analytical approach for this system.

Findings

Existence of infinitely many modulated amplitude waves.

These waves are generally unstable.

Numerical simulations support the analytical results.

Abstract

We apply the averaging method to analyze spatio-temportal structures in nonlinear Schr\"odinger equations and thereby study the dynamics of quasi-one-dimensional collisionally inhomogeneous Bose-Einstein condensates with the scattering length varying periodically in spatial and crossing zero. Infinitely many (positive measure set) modulated amplitude waves (periodic and quasi-periodic), which are instable, can be proved to exist by adjusting the intergration constant c on some open interval. Finally, some numerical simulations support our results.