Darboux transformation and rogue wave solutions for the variable-coefficients coupled Hirota equations
A Lax pair is a pair of linear operators, which is associated with a given partial differential equation. It is usually quite difficult to find the Lax pair corresponding to a given PDE. Therefore, often first the Lax pair is defined, and then the corresponding PDE is computed. For the Hirota equations in this article, possibly no Lax pair is known. The authors have a coupled Hirota equation (CH) and want to express this by using a DT (Darboux transformation). The CH system in [\textit{S. Chen} and \textit{L.-Yan Song}, ``Rogue waves in coupled Hirota systems'', Phys. Rev. E 87, No. 3 (2013; \url{doi:10.1103/physreve.87.032910})] is not the same as the one in equations 1 and 2 (which are not proved). The proofs use the AKNS technique and DT in explicit matrix form. Rough waves with multiple compression points are illustrated by pictures. Several abbreviations, which are used in the text are presented in the introduction.
variable-coefficients coupled Hirota equations
scientific article; zbMATH DE number 6682109
scientific article