Equations of Nonlinear Dispersive Long Waves for a Large Ursell Number

Equations of nonlinear dispersive long waves are derived for a large Ursell number in water of varying depth. The equations include nonlinear dispersive effects. Numerical simulation of solitary waves are carried out by using the present and conventional theories. From comparisons between numerical and experimental results where the present theory provides a better agreement, it is concluded that nonlinear effects of dispersive terms are significantly important for finite amplitude waves.