Linear superposition in nonlinear equations.
Several nonlinear systems such as the Korteweg-de Vries (KdV) and modified KdV equations and lambda phi(4) theory possess periodic traveling wave solutions involving Jacobi elliptic functions. We show that suitable linear combinations of these known periodic solutions yield many additional solutions with different periods and velocities. This linear superposition procedure works by virtue of some remarkable new identities involving elliptic functions.
Khare
Avinash
A
Department of Physics, University of Illinois at Chicago, Chicago, IL 60607-7059, USA.
Sukhatme
Uday
U