A method which can be used to solve the initial value problem for certain classes of nonlinear partial differential equations.
The method reduces the initial value problem
to a linear integral equation in which time
appears only implicitly. However, the solutions 
and various of their derivatives must approach zero as
(Infeld and Rowlands 2000).
Inverse Scattering Method
See also
Ablowitz-Ramani-Segur Conjecture, Bäcklund TransformationExplore with Wolfram|Alpha
References
Infeld, E. and Rowlands, G. "Inverse Scattering Method." §7.4 in Nonlinear Waves, Solitons, and Chaos, 2nd ed. Cambridge, England: Cambridge University Press, pp. 173-175, 2000.Miura, R. M.(Ed.). Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications. New York: Springer-Verlag, 1974.Referenced on Wolfram|Alpha
Inverse Scattering MethodCite this as:
Weisstein, Eric W. "Inverse Scattering Method." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/InverseScatteringMethod.html