Localized spatially nonlinear matter waves in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearity

TL;DR

This paper explores localized nonlinear matter wave solutions in atomic-molecular Bose-Einstein condensates with space-modulated nonlinearities, analyzing their properties, topological features, and stability influenced by various parameters.

Contribution

It introduces new Jacobi elliptic and rational solutions for atomic-molecular BECs with space-dependent nonlinearities and examines their topological and stability characteristics.

Findings

Localized solutions depend on quantum numbers and parameters.

Topological properties vary with coupling and quantum states.

Stability is influenced by chemical potential and detuning.

Abstract

The intrinsic nonlinearity is the most remarkable characteristic of the Bose-Einstein condensates (BECs) systems. Many studies have been done on atomic BECs with time- and space- modulated nonlinearities, while there is few work considering the atomic-molecular BECs with space-modulated nonlinearities. Here, we obtain two kinds of Jacobi elliptic solutions and a family of rational solutions of the atomic-molecular BECs with trapping potential and space-modulated nonlinearity and consider the effect of three-body interaction on the localized matter wave solutions. The topological properties of the localized nonlinear matter wave for no coupling are analysed: the parity of nonlinear matter wave functions depends only on the principal quantum number $n$, and the numbers of the density packets for each quantum state depend on both the principal quantum number $n$ and the secondary quantum number $l$. When the coupling is not zero,the localized nonlinear matter waves given by the rational function, their topological properties are independent of the principal quantum number $n$, only depend on the secondary quantum number $l$. The Raman detuning and the chemical potential can change the number and the shape of the density packets. The stability of the Jacobi elliptic solutions depends on the principal quantum number $n$, while the stability of the rational solutions depends on the chemical potential and Raman detuning.