We study the spectral structure of the complex linearized operator for a class of nonlinear Schrödinger systems, obtaining as byproduct some interesting properties of non-degenerate ground state of the associated elliptic system, such as being isolated and orbitally stable.

We demonstrate in a model independent way that, in the combined heavy-quark and large- N(c) limit, there exists a new contracted U(4) symmetry which connects orbitally excited heavy baryons to the ground states.

Using Bäcklund transformation the spectral property of the KP-I lump solution is completely analyzed. It is proved that the lump solution is nondegenerate and has Morse index one. As a consequence we show that it is orbitally stable.

The μ-Camassa–Holm (μCH) equation is a nonlinear integrable partial differential equation closely related to the Camassa–Holm equation. We prove that the periodic peaked traveling wave solutions (peakons) of the μCH equation are orbitally stable.