Nonlinear Sciences – Exactly Solvable and Integrable Systems
Scientific paper
2012-01-23
Nonlinear Sciences
Exactly Solvable and Integrable Systems
18 pages
Scientific paper
We present a discrete inverse scattering transform for all ABS equations excluding Q4. The nonlinear partial difference equations presented in the ABS hierarchy represent a comprehensive class of scalar affine-linear lattice equations which possess the multidimensional consistency property. Due to this property it is natural to consider these equations living in an N-dimensional lattice, where the solutions depend on N distinct independent variables and associated parameters. The direct scattering procedure, which is one-dimensional, is carried out along a staircase within this multidimensional lattice. The solutions obtained are dependent on all N lattice variables and parameters. We further show that the soliton solutions derived from the Cauchy matrix approach are exactly the solutions obtained from reflectionless potentials, and we give a short discussion on inverse scattering solutions of some previously known lattice equations, such as the lattice KdV equation.
No associations
LandOfFree
Multidimensional Inverse Scattering of Integrable Lattice Equations does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Multidimensional Inverse Scattering of Integrable Lattice Equations, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Multidimensional Inverse Scattering of Integrable Lattice Equations will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-496330