The objective of this paper is to investigate the nonlinear dispersion Drinfel’d-Sokolov  equation. Compactons, solitons, solitary patterns, periodic solutions and algebraic traveling wave solutions are expressed analytically under various circumstances. The conditions that cause the qualitative change in the physical structures of the solutions are emphasized.

the nonlinear dispersion Drinfel’d-Sokolov system, compactons, solitons, variants, periodic solutions.