A Five-Component Generalized mKdV Equation and Its Exact Solutions

Bo Xue, Huiling Du and Ruomeng Li
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Bo Xue: School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, China
Huiling Du: School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, China
Ruomeng Li: School of Mathematics and Statistics, Zhengzhou University, 100 Kexue Road, Zhengzhou 450001, China

Mathematics, 2020, vol. 8, issue 7, 1-12

Abstract: In this paper, a 3 × 3 spectral problem is proposed and a five-component equation that consists of two different mKdV equations is derived. A Darboux transformation of the five-component equation is presented relating to the gauge transformations between the Lax pairs. As applications of the Darboux transformations, interesting exact solutions, including soliton-like solutions and a solution that consists of rational functions of e x and t , for the five-component equation are obtained.

Keywords: gauge transformation; Darboux transformation; explicit solution (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2020
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