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

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.

MSC:

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