  We present a general result of transverse nonlinear instability of 1-d
solitary waves for Hamiltonian PDE's for both periodic or localized transverse
perturbations. Our main structural assumption is that the linear part of the 1d
model and the transverse perturbation "have the same sign". Our result applies
to the generalized KP-I equation, the Nonlinear Schr\"odinger equation, the
generalized Boussinesq system and the Zakharov-Kuznetsov equation and we hope
that it may be useful in other contexts.
