Existence of bounds for dark solitons in a class of nonlinear Schrodinger equations: explicit upper and lower bounds.
J. Belmonte-Beitia
Mathematical Methods in the Applied Sciences, 36, 8, 974-982 (2013).
MOLAB authors
Belmonte Beitia, Juan. 
Abstract
The dark soliton solutions corresponds to certain heteroclinic orbits for related autonomous planar differential equations. In this paper, we give a proof of the existence of upper and lower bounds of these heteroclinic orbits and find these bounds of explicit form. We put it into practice for a particular case of the derivative nonlinear Schrödinger equation