The propagation of rumors is a complex and varied phenomenon. In the process of rumor dissemination, in addition to rumor claims, there will be abundant social context information surrounding the rumor. Therefore, it is vital to learn the characteristics of rumors in terms of both a linear temporal sequence and non-linear diffusion structure simultaneously. However, in some recent research, time-dependent and diffusion-related information has not been fully utilized. Accordingly, in this paper, we propose a novel model Rumor Detection with Field of Linear and Non-Linear Propagation (RDLNP), which attempts to detect rumors from the above two fields automatically by taking advantage of claim content, social context and temporal information. First, the rumor hybrid feature learning (RHFL) we designed can extract the correlations of claims and temporal information in order to differentiate the hybrid features of specific posts and generate unified node embedding for rumors. Second, we proposed non-linear structure learning (NLSL) and linear sequence learning (LSL) to integrate contextual features along the path of the diffusion structure and the temporal engagement variation of responses respectively. Moreover, the introduction of stance attention grants the LSL have the ability to flexibly capture the dependency between the source node and the child nodes. Finally, shared feature learning (SFL) models the representation reinforcement and mutual influence between NLSL and LSL, then highlights their valuable features. Experiments conducted on two public and widely used datasets, i.e. PHEME and RumorEval, demonstrate both the effectiveness and the outstanding performance of the proposed approach.