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.