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To construct doubly periodic wave solutions, we extend the generalized <jats:italic>F<\/jats:italic>\u2010expansion method for the first time to the tdcWBK system. As a result, many new Jacobi elliptic doubly periodic solutions are obtained; the limit forms of which are the hyperbolic function solutions and trigonometric function solutions. It is shown that the original <jats:italic>F<\/jats:italic>\u2010expansion method cannot derive Jacobi elliptic doubly periodic solutions of the tdcWBK system, but the novel approach of this paper is valid. To gain more insight into the doubly periodic waves contained in the tdcWBK system, we simulate the dynamical evolutions of some obtained Jacobi elliptic doubly periodic solutions. The simulations show that the doubly periodic waves possess time\u2010varying amplitudes and velocities as well as singularities in the process of propagations.<\/jats:p>","DOI":"10.1155\/2018\/3158126","type":"journal-article","created":{"date-parts":[[2018,8,29]],"date-time":"2018-08-29T10:55:13Z","timestamp":1535540113000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["A Novel Approach to a Time\u2010Dependent\u2010Coefficient WBK System: Doubly Periodic Waves and Singular Nonlinear Dynamics"],"prefix":"10.1155","volume":"2018","author":[{"ORCID":"https:\/\/orcid.org\/0000-0002-7956-4882","authenticated-orcid":false,"given":"Bo","family":"Xu","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-4631-7033","authenticated-orcid":false,"given":"Sheng","family":"Zhang","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2018,8,28]]},"reference":[{"volume-title":"Report on Waves, Fourteen Meeting of the British Association for the Advancement of Science","year":"1844","author":"Russell J. 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