Linear Superposition in Nonlinear Equations

Avinash Khare, Uday Sukhatme

Published 2001-11-30Version 1

Even though the KdV and modified KdV equations are nonlinear, we show that suitable linear combinations of known periodic solutions involving Jacobi elliptic functions yield a large class of additional solutions. This procedure works by virtue of some remarkable new identities satisfied by the elliptic functions.