Symmetries for exact solutions to the nonlinear Schrödinger equation. (English) Zbl 1189.37074

Aktosun, Tuncay; Busse, Theresa; Demontis, Francesco; van der Mee, Cornelis

J. Phys. A, Math. Theor. 43, No. 2, Article ID 025202, 14 p. (2010).

For the focusing cubic Schrödinger equation \[ iu_t+u_{xx}+2|u|^2u=0, \] a symmetry is discussed in expressing exact solutions in terms of constant parameters. The results are generalized for the matrix case.

Reviewer: Vjacheslav Yurko (Saratov)

MSC:

37K15	Inverse spectral and scattering methods for infinite-dimensional Hamiltonian and Lagrangian systems
35Q51	Soliton equations
35Q55	NLS equations (nonlinear Schrödinger equations)

Keywords:

nonlinear integrable equations; exact solutions; inverse scattering