Ground state of the one dimensional Gross-Pitaevskii equation with a Morse potential

TL;DR

This paper investigates the ground state properties of the one-dimensional Gross-Pitaevskii equation with a Morse potential, revealing a critical coupling where the bound state disappears, akin to a saddle node bifurcation.

Contribution

It introduces a variational approach to analyze the ground state and identifies the critical coupling constant for state disappearance in the system.

Findings

Ground state ceases to be bound at a critical coupling.

Disappearance of the ground state resembles a saddle node bifurcation.

Provides insight into nonlinear quantum systems with Morse potential.

Abstract

We have studied the ground state of the Gross-Pitaevskii equation (nonlinear Schrodinger equation) for a Morse potential via a variational approach. It is seen that the ground state ceases to be bound when the coupling constant of the nonlinear term reaches a critical value. The disappearence of the ground state resembles a saddle node bifurcation.