The landscape evolution of active orogens can be regarded as the coupling between climatic change and tectonic movement. Rivers originating from and flowing through orogens have been affected and reshaped by regional rock uplift and deformation. The related tectonic signals, as a result, can be recorded and stored in stream longitudinal profiles. The stream-power river incision model, combing bedrock uplift, river incision, and topographic evolution,makes it possible to extract the spatial and temporary details of rock uplift. The well known stream-power river incision model is expressed as a non-linear partial differential equation (PDE),in which the temporal variation of bedrock channel elevation is the competition between rock uplift and channel incision. During the past 40 years, studies had been on its steady-state form. Assuming that the river profile is under a steady state with spatially invariant rock uplift, a power-law scaling between channel slope and drainage area can be derived. Then, a steepness index is yielded to quantify the spatial pattern of rock uplift rates. However, the landforms in active orogens are usually in a transient state where rock uplift cannot be balanced by river incision. With the development of mathematics and computer science, more and more scholars have been working on the solutions(both analytical and numerical) of the transient PDE. Based on the stream power incision model (allowing both spatially and temporarily variant rock uplift and a non-linear relationship between river incision and channel gradient), the velocity of knickpoint migration was derived. Then, the landscape response time could be calculated by dividing the river length by the horizontal velocity of knickpoint migration. Both knickpoint migration velocity and landscape time vary a lot between linear and non-linear conditions. For the linear condition,knickpoints migrate upstream in the same horizontal velocity that depends on erodibility and drainage area. The landscape response time shows no relation with rock uplift rate. Thus, the "older" knickpoints cannot be erased by "younger" ones, leaving a full rock uplift history. To model the rock uplift history, the chi-z plot is divided into a series of segments. Each segment can be regarded as a normalized time interval and elevation difference. By dividing the elevation difference by time interval, we can get the transformed rock uplift rate at the specified time. While for the non-linear condition, the horizontal velocities of knickpoints migrating upstream vary largely. Those "older" knickpoints might be erased by "younger" ones. The landscape response time depends on the rock uplift rates before and after the tectonic event. Therefore,some details of rock uplift will be lost owing to the non-uniform velocities. Assuming spatially invariant rock uplift, the analytical solution to the PDE was derived. For two conditions(n< 1, rock uplift rate increases, or n>1, rock uplift rate decreases), a full rock uplift history will be stored and a "stretch zone" was present along the chi-z plot. When n> 1, rock uplift rate decreases, or n< 1, rock uplift rate increases,the "slope patch" generated elder will be partly eased,resulting into a "consuming knickpoint". However, spatial information from the non-linear transient equation is still confusing.