Soliton Molecules, Rational Positon Solution and Rogue Waves for the Extended Complex Modied KdV Equation Lin Huang Hangzhou Dianzi University Nannan Lv (
[email protected] ) Hangzhou Dianzi University School of Science Research Article Keywords: Darboux transformation, Soliton molecule, Positon solution, Rational positon solution, Rogue waves solution Posted Date: May 11th, 2021 DOI: https://doi.org/10.21203/rs.3.rs-434604/v1 License: This work is licensed under a Creative Commons Attribution 4.0 International License. Read Full License Version of Record: A version of this preprint was published at Nonlinear Dynamics on August 5th, 2021. See the published version at https://doi.org/10.1007/s11071-021-06764-x. Soliton molecules, rational positons and rogue waves for the extended complex modified KdV equation Lin Huang ∗and Nannan Lv† School of Science, Hangzhou Dianzi University, 310018 Zhejiang, China. May 6, 2021 Abstract We consider the integrable extended complex modified Korteweg–de Vries equation, which is generalized modified KdV equation. The first part of the article considers the construction of solutions via the Darboux transformation. We obtain some exact solutions, such as soliton molecules, positon solutions, rational positon solutions, and rogue waves solutions. The second part of the article analyzes the dynamics of rogue waves. By means of the numerical analysis, under the standard decomposition, we divide the rogue waves into three patterns: fundamental pattern, triangular pattern and ring pattern. For the fundamental pattern, we define the length and width of the rogue waves and discuss the effect of different parameters on rogue waves. Keywords: Darboux transformation, Soliton molecule, Positon solution, Rational positon so- lution, Rogue waves solution.