Solitary wave solutions (solitons) were first observed in the water by John Scott Russell in 1834 and nowadays attract a lot of attention in many nonlinear physical and biological systems. Solitons require a balance between dispersion and nonlinearity, and usually form families with different amplitudes. The importance of solitons is underlined by the so-called soliton resolution conjecture: roughly speaking, the conjecture says that all reasonable (finite energy) solutions to nonlinear dispersive PDEs resolve into a superposition of radiation (which behaves like a solution of a linear Schroedinger equation) and a finite number of solitons.