{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,2]],"date-time":"2025-12-02T03:12:42Z","timestamp":1764645162265,"version":"3.41.2"},"reference-count":36,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T00:00:00Z","timestamp":1346716800000},"content-version":"vor","delay-in-days":247,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"content-domain":{"domain":["onlinelibrary.wiley.com"],"crossmark-restriction":true},"short-container-title":["Journal of Applied Mathematics"],"published-print":{"date-parts":[[2012,1]]},"abstract":"<jats:p>The two variables (<jats:italic>G<\/jats:italic><jats:sup>\u2032<\/jats:sup>\/<jats:italic>G<\/jats:italic>, 1\/<jats:italic>G<\/jats:italic>)\u2010expansion method is proposed in this paper to construct new exact traveling wave solutions with parameters of the nonlinear (3 + 1)\u2010dimensional Kadomtsev\u2010Petviashvili equation. This method can be considered as an extension of the basic (<jats:italic>G<\/jats:italic><jats:sup>\u2032<\/jats:sup>\/<jats:italic>G<\/jats:italic>)\u2010expansion method obtained recently by Wang et al. When the parameters are replaced by special values, the well\u2010known solitary wave solutions and the trigonometric periodic solutions of this equation were rediscovered from the traveling waves.<\/jats:p>","DOI":"10.1155\/2012\/560531","type":"journal-article","created":{"date-parts":[[2012,9,4]],"date-time":"2012-09-04T21:01:12Z","timestamp":1346792472000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":32,"title":["Traveling Wave Solutions of the Nonlinear (3 + 1)\u2010Dimensional Kadomtsev\u2010Petviashvili Equation Using the Two Variables (<i>G<\/i><sup>\u2032<\/sup>\/<i>G<\/i>, 1\/<i>G<\/i>)\u2010Expansion Method"],"prefix":"10.1155","volume":"2012","author":[{"given":"E. M. 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