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 Method## Explore 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 Conjecture## Cite this as:

Weisstein, Eric W. "Ablowitz-Ramani-Segur Conjecture."
From *MathWorld*--A Wolfram Web Resource. https://mathworld.wolfram.com/Ablowitz-Ramani-SegurConjecture.html