37 citations · 79 across the 3 of their papers we have counts for
3 papers
math.CA2008★ 15 cited
On the Linearization of the First and Second Painleve' Equations
N. Joshi, A. V. Kitaev, P. A. Treharne
We found Fuchs--Garnier pairs in 3X3 matrices for the first and second Painleve' equations which are linear in the spectral parameter. As an application of our pairs for the second…
math.CA2007★ 37 cited
On the Linearization of the Painleve' III-VI Equations and Reductions of the Three-Wave Resonant System
N. Joshi, A. V. Kitaev, P. A. Treharne
We extend similarity reductions of the coupled (2+1)-dimensional three-wave resonant interaction system to its Lax pair. Thus we obtain new 3x3 matrix Fuchs--Garnier pairs for the…
nlin.SI2006★ 27 cited
The Generalized Dirichlet to Neumann map for the KdV equation on the half-line
P. A. Treharne, A. S. Fokas
For the two versions of the KdV equation on the positive half-line an initial-boundary value problem is well posed if one prescribes an initial condition plus either one boundary c…