Applicability of the 3^rd order theoretical solutions for internal waves in a two-layer system is investigated by using a strongly nonlinear and dispersive internal wave model. The 3^rd order solution is derived using the 9^th order internal wave equations. The 3^rd order solution is found to give larger wavelength scale compared to KdV theory. The applicability of the 3^rd order solution is confirmed to be high when the amplitude of internal solitary wave is 5% of the lower layer thickness. A fully nonlinear strongly dispersive internal wave model reveals that high frequency internal waves are induced behind an internal solitary wave when the initial shape of internal solitary wave is larger than critical level.