Finite amplitude ultra-long waves tinder the effect of heat source are studied.The conditions for the existence of finite amplitude periodicity and solitaryperiodicity ultra-longwaves are obtained based oi1 the Hamilton’s function and total energy variation.followed bythe wave analytical solution found by use of Hamilton function for motion invariance and function approximation.It is noted that there is no solitary wave:solution for these ultra-long waves nor constraints of horizontal divergence without the effect of heat source and vice versa.