Inverse Scattering Method

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 $u(x,t)$ and various of their derivatives must approach zero as $x\to\pm\infty$ (Infeld and Rowlands 1990).

See also Ablowitz-Ramani-Segur Conjecture, Bäcklund Transformation

References

Infeld, E. and Rowlands, G. ``Inverse Scattering Method.'' §7.4 in Nonlinear Waves, Solitons, and Chaos. Cambridge, England: Cambridge University Press, pp. 192-196, 1990.

Miura, R. M. (Ed.) Bäcklund Transformations, the Inverse Scattering Method, Solitons, and Their Applications. New York: Springer-Verlag, 1974.