Helmholtz solitons : Maxwell equations , interface geometries and vector regimes

In this paper, we give an overview of new results in Helmholtz soliton theory. Firstly, fundamental considerations are made in terms of new contexts for Helmholtz solitons that arise directly from Maxwell's equations. We then detail applications involving a variety of different material interfaces and the role of Helmholtz solitons in these configurations. Finally, specific new families of solutions arising from the generalisation of the Manakov equation are reported.