Linear Superposition in Nonlinear Equations
Mathematical Physics
2009-11-07 v1 Condensed Matter
High Energy Physics - Theory
Analysis of PDEs
math.MP
Exactly Solvable and Integrable Systems
Quantum Physics
Abstract
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.
Cite
@article{arxiv.math-ph/0112002,
title = {Linear Superposition in Nonlinear Equations},
author = {Avinash Khare and Uday Sukhatme},
journal= {arXiv preprint arXiv:math-ph/0112002},
year = {2009}
}
Comments
7 pages, 1 figure