The modeling of unidirectional propagation of long water waves in dispersive media is presented. The Korteweg-de Vries (KdV) and Benjamin-Bona-Mahony (BBM) equations are derived from water waves models. New traveling solutions of the KdV and BBM equations are obtained by implementing the extended direct algebraic and extended sech-tanh methods. The stability of the obtained traveling solutions is analyzed and discussed.
A. R. Seadawy. A. Sayed. "Traveling Wave Solutions of the Benjamin-Bona-Mahony Water Wave Equations." Abstr. Appl. Anal. 2014 (SI09) 1 - 7, 2014. https://doi.org/10.1155/2014/926838