What do solitons of the Nonlinear Schrodinger equation look like?
Try the following text book: – Semiclasical Solitron Ensembles for the Focussing Nonlinear Schrodinger Equation, Kamvissis McLaughlin & Muller, Princeton University Press, 2003. ISBN 0-691-11482-X pbk Page 66, section 4.3.4 Properties of the semi classical solution of the Nonlinear Schrodinger equation, onwards… This book is written for mathematicians and therefore uses a Riemann surface approach to the solution you are looking for. However, the pages 66 onwards adopt elements of your notation. The solutions revolve around the conservation of waves in terms of a train of wavenumbers. The ‘cut’ matrix solutions use the real part of the eigenfunction but the elements are premuliplied by a complex exponential term.
