{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,3,17]],"date-time":"2026-03-17T16:40:23Z","timestamp":1773765623649,"version":"3.50.1"},"reference-count":58,"publisher":"Wiley","issue":"1","license":[{"start":{"date-parts":[[2012,8,16]],"date-time":"2012-08-16T00:00:00Z","timestamp":1345075200000},"content-version":"vor","delay-in-days":228,"URL":"http:\/\/creativecommons.org\/licenses\/by\/3.0\/"}],"funder":[{"DOI":"10.13039\/501100004595","name":"Universiti Sains Malaysia","doi-asserted-by":"publisher","award":["304\/PMATHS\/6310072"],"award-info":[{"award-number":["304\/PMATHS\/6310072"]}],"id":[{"id":"10.13039\/501100004595","id-type":"DOI","asserted-by":"publisher"}]}],"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>we apply the improved  (<jats:italic>G<\/jats:italic><jats:sup>\u2032<\/jats:sup>\/<jats:italic>G<\/jats:italic>)\u2010expansion method for constructing abundant new exact traveling wave solutions of the (2+1)\u2010dimensional Modified Zakharov\u2010Kuznetsov equation.  In addition, <jats:italic>G<\/jats:italic><jats:sup>\u2033<\/jats:sup> + <jats:italic>\u03bb<\/jats:italic><jats:italic>G<\/jats:italic><jats:sup>\u2032<\/jats:sup> + <jats:italic>\u03bc<\/jats:italic><jats:italic>G<\/jats:italic> = 0 together with  is employed in this method, where <jats:italic>p<\/jats:italic><jats:sub><jats:italic>q<\/jats:italic><\/jats:sub> (<jats:italic>q<\/jats:italic> = 0, \u00b11, \u00b12, \u2026, \u00b1<jats:italic>w<\/jats:italic>), <jats:italic>\u03bb<\/jats:italic> and <jats:italic>\u03bc<\/jats:italic> are constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.<\/jats:p>","DOI":"10.1155\/2012\/438928","type":"journal-article","created":{"date-parts":[[2012,8,16]],"date-time":"2012-08-16T21:01:19Z","timestamp":1345150879000},"update-policy":"https:\/\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":13,"title":["The Improved (<i>G<\/i>\u2019\/<i>G<\/i>)\u2010Expansion Method for the (2+1)\u2010Dimensional Modified Zakharov\u2010Kuznetsov Equation"],"prefix":"10.1155","volume":"2012","author":[{"given":"Hasibun","family":"Naher","sequence":"first","affiliation":[]},{"given":"Farah Aini","family":"Abdullah","sequence":"additional","affiliation":[]}],"member":"311","published-online":{"date-parts":[[2012,8,16]]},"reference":[{"key":"e_1_2_7_1_2","series-title":"Mathematics in Science and Engineering","volume-title":"B\u00e4cklund Transformations and Their Applications","author":"Rogers C.","year":"1982"},{"key":"e_1_2_7_2_2","doi-asserted-by":"publisher","DOI":"10.1017\/CBO9780511623998"},{"key":"e_1_2_7_3_2","doi-asserted-by":"publisher","DOI":"10.1016\/0375-9601(96)00283-6"},{"key":"e_1_2_7_4_2","doi-asserted-by":"publisher","DOI":"10.1103\/PhysRevLett.27.1192"},{"key":"e_1_2_7_5_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00580-1"},{"key":"e_1_2_7_6_2","doi-asserted-by":"publisher","DOI":"10.1155\/2011\/575679"},{"key":"e_1_2_7_7_2","doi-asserted-by":"publisher","DOI":"10.1155\/2012\/710375"},{"key":"e_1_2_7_8_2","doi-asserted-by":"publisher","DOI":"10.1016\/S0375-9601(01)00376-0"},{"key":"e_1_2_7_9_2","doi-asserted-by":"publisher","DOI":"10.1119\/1.17120"},{"key":"e_1_2_7_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.amc.2006.11.013"},{"key":"e_1_2_7_11_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.cnsns.2008.07.004"},{"key":"e_1_2_7_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2004.09.044"},{"key":"e_1_2_7_13_2","doi-asserted-by":"publisher","DOI":"10.1016\/j.chaos.2005.09.030"},{"key":"e_1_2_7_14_2","first-page":"274","article-title":"New exact solutions of nonlinear variants of the RLW, and PHI-four and Boussinesq equations based on modified extended direct algebraic method","volume":"7","author":"Soliman A. 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