Darboux transformation of the general Hirota equation: multisoliton solutions, breather solutions, and rogue wave solutions

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• 作者：Deng-Shan Wang ; Fei Chen ; Xiao-Yong Wen
• 关键词：Darboux transformation ; multisoliton solutions ; breather solutions ; rogue wave solutions ; optical fibers
• 刊名：Advances in Difference Equations
• 出版年：2016
• 出版时间：December 2016
• 年：2016
• 卷：2016
• 期：1
• 全文大小：7,408 KB
• 刊物主题：Difference and Functional Equations; Mathematics, general; Analysis; Functional Analysis; Ordinary Differential Equations; Partial Differential Equations;
• 出版者：Springer International Publishing
• ISSN：1687-1847

文摘

In this paper, we investigate the exact solutions and conservation laws of a general Hirota equation. Firstly, the N-fold Darboux transformation of this equation is proposed. Then by choosing three kinds of seed solutions, the multisoliton solutions, breather solutions, and rogue wave solutions of the general Hirota equation are obtained based on the Darboux transformation. Finally, the conservation laws of this equation are derived by using its linear spectral problem. The results in this paper may be useful in the study of ultrashort optical solitons in optical fibers.