We consider dispersion generalized nonlinear Schrödinger equations (NLS) of the form i∂tu = P (D)u − |u| 2σ u, where P (D) denotes a (pseudo)-differential operator of arbitrary order. As a main result, we prove symmetry results for traveling solitary waves in the case of powers σ ∈ N. The arguments are based on Steiner type rearrangements in Fourier space. Our results apply to a broad class of NLS-type equations such as fourthorder (biharmonic) NLS, fractional NLS, square-root Klein-Gordon and half-wave equations.

No abstract

No abstract