A. Contreras, D.E. Pelinovsky, and M. Plum
Orbital stability of domain walls in coupled Gross-Pitaevskii systems
SIAM Journal of Mathematical Analysis 50, 810-833 (2018)
Domain walls are minimizers of energy for coupled one-dimensional Gross-Pitaevskii
systems with nontrivial boundary conditions at infinity. It has been shown previously that these
solutions are orbitally stable in the space of complex H1 functions with the same limits at
infinity. In the present work we adopt a new weighted H1 space to control perturbations
of the domain walls and thus to obtain an improved orbital stability result. A major
difficulty arises from the degeneracy of linearized operators at the domain walls and the
lack of coercivity.
coupled Gross--Pitaevskii equations, domain walls, orbital stability, coercivity of energy.