Two Nonlinear Long Wave Models in Shallow Water Generated by Applied Pressure - Parvin, M. S.; Sultana, M. S.; Sarker, M. S. Alam (IJRDO -JOURNAL OF MATHEMATICS, 2018)
Water wave motion is described by the velocity potential for three dimensional viscous, incompressible and irrotational flow. Using dynamic and kinematic free surface conditions from Navier-Stokes equations, the nonlinear long wave models are generated by a disturbance moving at subcritical, critical and supercritical speed in unbounded shallow water. Nonlinearity  and the dispersion  are related as  , where nonlinearity is less than one. Then new forms of two long wave models are established in which nonlinear terms are expressed by the derivative of depth averaged velocity potential. The implements of the numerical algorithm are studied in the later section.