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.
- traveling waves