Linear non-degeneracy of the 1d blow-up limit in the phase segregation of Bose-Einstein condensates

TL;DR

This paper proves that the linearized blow-up problem at the interface in 1D phase segregation of Bose-Einstein condensates has a one-dimensional kernel, extending known results from lower dimensions.

Contribution

It establishes the non-degeneracy of the linearization at the interface in one dimension, a property previously known only in lower dimensions.

Findings

Kernel of linearization is one-dimensional

Generated by translations normal to the interface

Extends non-degeneracy results to 1D case

Abstract

We show that the kernel of the linearization of the blow-up problem at the regular part of the interface that separates segregated BECs is one-dimensional, generated by translations in the normal direction to the interface. This useful non-degeneracy property was previously known only in one and two dimensions.