The Ablowitz-Ramani-Segur conjecture states that a nonlinear partial differential equation is solvable by the inverse scattering method only if every nonlinear ordinary differential equation obtained by exact reduction has the Painlevé property.
Ablowitz-Ramani-Segur Conjecture
See also
Inverse Scattering MethodExplore with Wolfram|Alpha
References
Tabor, M. Chaos and Integrability in Nonlinear Dynamics: An Introduction. New York: Wiley, p. 351, 1989.Referenced on Wolfram|Alpha
Ablowitz-Ramani-Segur ConjectureCite this as:
Weisstein, Eric W. "Ablowitz-Ramani-Segur Conjecture." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Ablowitz-Ramani-SegurConjecture.html