Abstract
This paper secures solitary waves and conservation laws to the familiar Korteweg-de Vries equation and Gardner's equation with three dispersion sources. The traveling wave hypothesis leads to the emergence of such waves. The three sources of dispersion are spatial dispersion, spatio-temporal dispersion and the dual-emporal-spatial dispersion. The conservation laws are enumerated for these models, evolved from the multiplier approach. The conserved quantities are computed with the solitary wave solutions that were recovered.