Abstract
It is shown that the prolongation structure theory for nonlinear (evolution) equations with two independent variables can be generalized to the systems with many independent variables. By means of the nonlinear realization theory of gauge symmetries, the fundamental equations for prolongation structures and the requirements for the generalized Lax representations of the nonlinear systems in higher dimensions have been given. Based upon the invariances of the prolongation structures or the generalized Lax representation under certain transformations, the general condition satisfied by the auto-Bäcklund transformations has been proposed and searching for a kind of auto-Bäcklund transformations has been transferred to solving the regular Riemann-Hilbert problem.
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.
