With the rapid development of Internet and Web techniques, Cross-Domain Recommendation (CDR) models have been widely explored for resolving the data-sparsity and cold-start problem. Meanwhile, most CDR models should utilize explicit domain-shareable information (e.g., overlapped users or items) for knowledge transfer across domains. However, this assumption may not be always satisfied since users and items are always non-overlapped in real practice. The performance of many previous works will be severely impaired when these domain-shareable information are not available. To address the aforementioned issues, we propose the Joint Preference Exploration and Dynamic Embedding Transportation model (JPEDET) in this paper which is a novel framework for solving the CDR problem when users and items are non-overlapped. JPEDET includes two main modules, i.e., joint preference exploration module and dynamic embedding transportation module. The joint preference exploration module aims to fuse rating and review information for modelling user preferences. The dynamic embedding transportation module is set to share knowledge via neural ordinary equations for dual transformation across domains. Moreover, we innovatively propose the dynamic transport flow equipped with linear interpolation guidance on barycentric Wasserstein path for achieving accurate and bidirectional transformation. Our empirical study on Amazon datasets demonstrates that JPEDET significantly outperforms the state-of-the-art models under the CDR setting.