Exact solutions of a generalized variant of the derivative nonlinear Schrödinger equation in a Scarff II external potential and their stability properties
Abstract
We obtain exact solitary wave solutions of a variant of the generalized derivative nonlinear Schrödinger equation in 1+1 dimensions with arbitrary values of the nonlinearity parameter κ in a ScarfII potential. This variant of the usual derivative nonlinear Schrödinger equation has the properties that for real external potentials, the dynamics is derivable from a Lagrangian. The solitary wave and trapped solutions have the same form as those of the usual derivative nonlinear Schrödinger equation. We show that the solitary wave solutions are orbitally stable for . We find new exact nodeless solutions to the bound states in the external complex potential which are related to the static solutions of the equation. We also use a collective coordinate approximation to analyze the stability of the trapped solutions when the external potential is real.
 Publication:

Journal of Physics A Mathematical General
 Pub Date:
 November 2018
 DOI:
 10.1088/17518121/aae1cf
 arXiv:
 arXiv:1805.04059
 Bibcode:
 2018JPhA...51R5203K
 Keywords:

 Nonlinear Sciences  Pattern Formation and Solitons
 EPrint:
 26 pages, 4 figures