A Five-Component Generalized mKdV Equation and Its Exact Solutions - Bo Xue (Mathematics, 2020)
In this paper, a <semantics> 3 × 3 </semantics> 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 <semantics> e x </semantics> and t, for the five-component equation are obtained.