Darboux transformation with Dihedral reduction group
نویسندگان
چکیده
We construct the Darboux transformation with Dihedral reduction group for the 2–dimensional generalisation of the periodic Volterra lattice. The resulting Bäcklund transformation can be viewed as a nonevolutionary integrable differential difference equation. We also find its generalised symmetry and the Lax representation for this symmetry. Using formal diagonalisation of the Darboux matrix we obtain local conservation laws of the system.
منابع مشابه
New Darboux Transformation for Hirota-Satsuma coupled KdV System
A new Darboux transformation is presented for the Hirota-Satsuma coupled KdV system. It is shown that this Darboux transformation can be constructed by means of two methods: Painlevé analysis and reduction of a binary Darboux transformation. By iteration of the Darboux transformation, the Grammian type solutions are found for the coupled KdV system.
متن کاملThe Solutions of the NLS Equations with Self-Consistent Sources
We construct the generalized Darboux transformation with arbitrary functions in time t for the AKNS equation with self-consistent sources (AKNSESCS) which, in contrast with the Darboux transformation for the AKNS equation, provides a non-auto-Bäcklund transformation between two AKNSESCSs with different degrees of sources. The formula for N-times repeated generalized Darboux transformation is pr...
متن کاملBäcklund–Darboux Transformations and Discretizations of Super KdV Equation
For a generalized super KdV equation, three Darboux transformations and the corresponding Bäcklund transformations are constructed. The compatibility of these Darboux transformations leads to three discrete systems and their Lax representations. The reduction of one of the Bäcklund–Darboux transformations and the corresponding discrete system are considered for Kupershmidt’s super KdV equation....
متن کاملDarboux transformations for twisted so(p,q) system and local isometric immersion of space forms
For the n-dimensional integrable system with a twisted so(p, q) reduction, Darboux transformations given by Darboux matrices of degree 2 are constructed explicitly. These Darboux transformations are applied to the local isometric immersion of space forms with flat normal bundle and linearly independent curvature normals to give the explicit expression of the position vector. Some examples are g...
متن کاملReduced Vectorial Ribaucour Transformation for the Darboux-Egoroff Equations
The vectorial fundamental transformation for the Darboux equations is reduced to the symmetric case. This is combined with the orthogonal reduction of Lamé type to obtain those vectorial Ribaucour transformations which preserve the Egoroff reduction. We also show that a permutability property holds for all these transformations. Finally, as an example, we apply these transformations to the Cart...
متن کامل