Abstract
A study of fully discretized lattice equations associated with the KdV hierarchy is presented. Loop group methods give a systematic way of constructing discretizations of the equations in the hierarchy. The lattice KdV system of Nijhoff et al arises from the lowest order discretization of the trivial, lowest order equation in the hierarchy, bt = bx. Two new discretizations are also given, the lowest order discretization of the first nontrivial equation in the hierarchy, and a `second order' discretization of bt = bx. The former, which is given the name full lattice KdV, has the (potential) KdV equation as a standard continuum limit. For each discretization a Bäcklund transformation is given and the soliton content is analysed. The full lattice KdV system has, like KdV itself, solitons of all speeds, whereas both other discretizations studied have a limited range of speeds (being discretizations of an equation with solutions only of a fixed speed).
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.
