A Rogue-Langmuir-type traveling wave continuous solution to nonlinearly   dispersive Schr\"{o}dinger equation using a polynomial expansion scheme
  In this paper, traveling wave solutions to the nonlinearly dispersive Schr\"odinger equation are given in the case of one-dimensional non-relativistic electron confined to a cylindrical quantum well. Investigations gave evidence to the possibility of implementing continuous solutions for a quantum-based problem. 
Karem Boubaker and Lin Zhang
math-ph math.FA math.MP