323 citations · 2.2k across the 48 of their papers we have counts for
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Singularity confinement and chaos in discrete systems
Jarmo Hietarinta, Claude Viallet
We present a number of second order maps, which pass the singularity confinement test commonly used to identify integrable discrete systems, but which nevertheless are non-integrab…
Pure quantum integrability
Jarmo Hietarinta
The correspondence between the integrability of classical mechanical systems and their quantum counterparts is not a 1-1, although some close correspondencies exist. If a classical…
Introduction to the Hirota bilinear method
J. Hietarinta
We give an elementary introduction to Hirota's direct method of constructing multisoliton solutions to integrable nonlinear evolution equations. We discuss in detail how this works…
Rational solutions to d-PIV
Jarmo Hietarinta, Kenji Kajiwara
We study the rational solutions of the discrete version of Painleve's fourth equation d-PIV. The solutions are generated by applying Schlesinger transformations on the seed solutio…
Inelastic Collision and Switching of Coupled Bright Solitons in Optical Fibers
R. Radhakrishnan, M. Lakshmanan, J. Hietarinta
By constructing the general six-parameter bright two-soliton solution of the integrable coupled nonlinear Schrodinger equation (Manakov model) using the Hirota method, we find that…
Painleve equations in terms of entire functions
Jarmo Hietarinta
In these lectures we discuss how the Painleve equations can be written in terms of entire functions, and then in the Hirota bilinear (or multilinear) form. Hirota's method, which h…