All Outputs (2)

The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases (2018)
Journal Article
Pickering, A., Gordoa, P. R., & Wattis, J. A. (2019). The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases. Physica D: Nonlinear Phenomena, 391, 72-86. https://doi.org/10.1016/j.physd.2018.12.001

In this paper we consider the matrix nonautonomous semidiscrete (or lattice) equation D dtUn = (2n − 1)(Un+1 − Un−1)−1, as well as the scalar case thereof. This equation was recently derived in the context of auto-Bäcklund transformations for a matri... Read More about The second Painlevé equation, a related nonautonomous semidiscrete equation, and a limit to the first Painlevé equation: scalar and matrix cases.

Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations (2018)
Journal Article
Wattis, J. A., Gordoa, P., & Pickering, A. (2018). Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations. Communications in Nonlinear Science and Numerical Simulation, 65, 98-110. https://doi.org/10.1016/j.cnsns.2018.05.016

We consider the first member of an extended modified Volterra lattice hierarchy. This system of equations is differential with respect to one independent variable and differential-delay with respect to a second independent variable. We use asymptot... Read More about Behaviour of the extended modified Volterra lattice --reductions to generalised mKdV and NLS equations.