Jacobi elliptic solutions, soliton solutions and other solutions to four higher-order nonlinear Schrodinger equations using two mathematical methods

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• 作者：Elsayed M.E. Zayed ; ^{eme_zayed@yahoo.com} ; Mona E.M. Elshater ^{mona_el.shater@yahoo.com}
• 关键词：(G&prime ; /G)-expansion method ; Extended auxiliary equation method ; Nonlinear Schrodinger equations ; Exact solutions ; Solitary wave solutions ; Jacobi elliptic function solutions ; Non-integer balance numbers
• 刊名：Optik - International Journal for Light and Electron Optics
• 出版年：2017
• 出版时间：February 2017
• 年：2017
• 卷：131
• 期：Complete
• 页码：1044-1062
• 全文大小：1328 K
• 卷排序：131

文摘

Two mathematical methods, via the (G′/G)-expansion method and extended auxiliary equation method are applied in this article to find many exact solutions with parameters of four higher-order nonlinear Schrodinger equations whose balance numbers are not positive integers, namely, the nonlinear Schrodinger equation with dual power-law nonlinearity, the higher-order dispersive nonlinear Schrodinger equation with both fourth-order dispersion effects and a quintic nonlinearity, the resonant nonlinear Schrodinger equation and the generalized higher-order nonlinear Schrodinger equation. When the parameters take up special values, the solitary and singular solitary wave solutions of these nonlinear Schrodinger equations are given. The used methods in this article present a wider applicability for handling nonlinear wave equations. Comparing our new results and the well-known results are obtained. Comparing the results resulting from the two methods with each others are also given.