We prove that standing-waves solutions to the non-linear Schrödinger equation in dimension one whose profiles can be obtained as minima of the energy over the mass, are orbitally stable and nondegenerate, provided the non-linear term G satisfies a Euler differential inequality. When the non-linear term G is a combined pure powertype, then there is only one positive, symmetric minimum of the energy constrained to the constant mass.

We show the existence of standing-wave solutions to a coupled non-linear Klein-Gordon equation. Our solutions are obtained as minimizers of the energy under a two-charges constraint. We prove that the ground state is stable and that standing-waves are orbitally stable under a non-degeneracy assumption.

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