2020/08/11 by Chen, Gong, Palacios, José M. · 2 citations
#Analysis of PDEs (math.AP) #FOS: Mathematics
paper · doi:10.48550/arxiv.2008.04812
In this work we study the orbital stability/instability in the energy space of a specific family of periodic wave solutions of the general ϕ4n-model for all n∈ℕ. This family of periodic solutions are orbiting around the origin in the corresponding phase portrait and, in the standing case, are related (in a proper sense) with the aperiodic Kink solution that connect the states -\tfrac12 with \tfrac12. In the traveling case, we prove the orbital instability in the whole energy space for all n∈ℕ, while in the standing case we prove that, under some additional parity assumptions, these solutions are orbitally stable for all n∈ℕ.