Abstract
We consider dispersion generalized nonlinear Schrödinger equations (NLS) of the form where 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 . The arguments are based on Steiner type rearrangements in Fourier space. Our results apply to a broad class of NLS-type equations such as fourth-order (biharmonic) NLS, fractional NLS, square-root Klein–Gordon and half-wave equations.
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