A numerical behavior of a KdV combined mKdV equation is obtained using the Melnikov method. Melnikov method is proved to be elegant, and successful alternative to characterizing the complex dynamics of multi-stable oscillators. Based on the Melnikov theory we present the homoclinic and heteroclinic orbits in the unperturbed system. It is show us whether the system is chaotic or not. In this work, we study the relation among the parameters of the linnonlinear dispersion term. Furthermore, we discuss the control threshold of the chaos. Chaos appear in the system due to the absence of damping term.

According on indigenous and exogenous economic factors, estimation of natural gas demands in industry sector from 1986 to 2013 will be discussed respectively, and the consumption of it will be predicted. In this study, structural time series models have been applied due to the considering exogenous economic factors, implicit Underlying Energy Demand Trend (UETD) which mainly are unobservable. Estimation's results imply on stochastic trend and demonstrate that uneconomical unobservable factors have effective role on featuring natural gas demand in industry sector.

Upward trend of UEDT indicate that industrial natural gas has been consumed in non-optimized way. In fact, the effects of unobservable factors on consumption of natural gas are positive. So, the resent result implicate that some unobservable factors like technology advancement, structural reforms, have failed in decreasing consumption of natural gas duo to not regarding some efficiency standards. The estimation's results confirm that natural gas relevant to all variable is inelasticity in a short-run, unlike long-run. The final results of estimation of industrial electricity demand it is predicted that Iran industrial natural gas demand will be 50 million m3 by 2021.