Abstract
We study Darboux and Laplace transformations of the solutions and potentials of the Goursat equation which is equivalent to one of the Lax pair equations for the 2D-MKdV hierarchy. The reduction restrictions for these transformations are considered. The derived reduction equations are generalizations of the Liouville and sinh-Gordon equation. The integrability of these equations by the ST method is proved. The binary Darboux transformation for the Goursat equation is suggested. We find exact rational nonsingular solutions of the 2D-MKdV equations via the Moutard transformation for the Goursat equation.
Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
