Since their discovery a mere thirty years ago, solitons have been invoked to explain such diverse phenomena as: The long lived ‘giant red spot’ in the highly turbulent Jovian atmosphere. The famous Fermi-Pasta-Ulam paradox wherein a nonlinearly coupled lattice of particles does not display the expected equipartition of energy among available modes. Ion-acoustic waves in a plasma. Energy storage and transfer in proteins via the Davydov soliton. The propagation of short laser pulses in optical fibres over long distances with negligible shape change. This new volume presents important research from around the globe.