18 research outputs found
Integrable discrete nets in Grassmannians
We consider discrete nets in Grassmannians which generalize
Q-nets (maps with planar elementary
quadrilaterals) and Darboux nets (-valued maps defined on the
edges of such that quadruples of points corresponding to
elementary squares are all collinear). We give a geometric proof of
integrability (multidimensional consistency) of these novel nets, and show that
they are analytically described by the noncommutative discrete Darboux system.Comment: 10 p
Breather lattice and its stabilization for the modified Korteweg-de Vries equation
We obtain an exact solution for the breather lattice solution of the modified
Korteweg-de Vries (MKdV) equation. Numerical simulation of the breather lattice
demonstrates its instability due to the breather-breather interaction. However,
such multi-breather structures can be stabilized through the concurrent
application of ac driving and viscous damping terms.Comment: 6 pages, 3 figures, Phys. Rev. E (in press
Generalized Darboux and Darboux-Levi transformations in 2+1 dimensions
SIGLEAvailable from British Library Document Supply Centre- DSC:DX174572 / BLDSC - British Library Document Supply CentreGBUnited Kingdo
Integrable discretization of hodograph-type systems,hyperelliptic integrals and Whitham equations
Discrete analogues of important objects and notions in the theory of semi-Hamiltonian systems of hydrodynamic type are presented