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In this paper, we construct twenty\u2010seven traveling wave solutions for the (2+1)\u2010dimensional modified Zakharov\u2010Kuznetsov equation by applying this method. Further, the auxiliary equation<jats:italic>G<\/jats:italic><jats:sup>\u2032<\/jats:sup>(<jats:italic>\u03b7<\/jats:italic>) =<jats:italic>w<\/jats:italic>+<jats:italic>u<\/jats:italic><jats:italic>G<\/jats:italic>(<jats:italic>\u03b7<\/jats:italic>) +<jats:italic>v<\/jats:italic><jats:italic>G<\/jats:italic><jats:sup>2<\/jats:sup>(<jats:italic>\u03b7<\/jats:italic>) is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.<\/jats:p>","DOI":"10.1155\/2012\/486458","type":"journal-article","created":{"date-parts":[[2012,12,11]],"date-time":"2012-12-11T21:00:49Z","timestamp":1355259649000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":19,"title":["New Traveling Wave Solutions by the Extended Generalized Riccati Equation Mapping Method of the (2 + 1)\u2010Dimensional Evolution Equation"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hasibun","family":"Naher","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Farah Aini","family":"Abdullah","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"311","published-online":{"date-parts":[[2012,12,11]]},"reference":[{"key":"e_1_2_7_1_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623998"},{"key":"e_1_2_7_2_2","volume-title":"Backlund Transformations and Their Applications","author":"Rogers C.","year":"1982"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.27.1192"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/363879"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/236875"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00580-1"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/575679"},{"key":"e_1_2_7_8_2","doi-asserted-by":"crossref","DOI":"10.1155\/2012\/710375","article-title":"Jacobi elliptic solutions for nonlinear differential difference equations in mathematical physics","volume":"2012","author":"Gepreel K. 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