Linear Superposition in Nonlinear Equations

Details Linear Superposition in Nonlinear Equations Linear Superposition in Nonlinear Equations

2001-11-30

arxiv.org/abs/math-ph/0112002v1

Phys.Rev.Lett. 88 (2002) 244101

Physics

Mathematical Physics

7 pages, 1 figure

Scientific paper

10.1103/PhysRevLett.88.244101

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.

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