Nonlinear dispersion and compact structures

Relaxing the distinguished ordering underlying the derivation of soliton supporting equations leads to new equations endowed with nonlinear dispersion crucial for the formation and coexistence of compactons, solitons with a compact support, and conventional solitons. Vibrations of the anharmonic mass-spring chain lead to a new Boussinesq equation admitting compactons and compact breathers. The model equation ut+[δu+3γu22+u1-ω(uωux)x] x+νutxx=0(ω,ν,δ,γconst) admits compactons and for 2ω=νγ=1 has a bi-Hamiltonian structure. The infinite sequence of commuting flows generates an integrable, compacton's supporting variant of the Harry Dym equation.