The Hirota method and soliton solutions to the multidimensional nonlinear Schrödinger equation.
The theory of differential invariants and KDV hamiltonian evolutions
Traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity: some results and open problems
This text is a survey of recent results on traveling waves for nonlinear Schrödinger equations with nonzero conditions at infinity. We present the existence, nonexistence and stability results and we describe the main ideas used in proofs.