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 $u_t+{\left[\frac{\delta u+3\mathrm{}\gamma u^2}{2+u^{1-\omega }{\left(u^{\omega }{u}_x\right)}_x}\right]}_x+\nu u_{\mathrm{txx}}=0(\omega ,\nu ,\delta ,\gamma \mathrm{const})$ admits compactons and for $2\omega =\nu \gamma =1\mathrm{}$ has a bi-Hamiltonian structure. The infinite sequence of commuting flows generates an integrable, compacton's supporting variant of the Harry Dym equation.

• Received 17 November 1993

DOI:https://doi.org/10.1103/PhysRevLett.73.1737