Phys. Rev. Lett. 88, 244101 (2002) [4 pages]Linear Superposition in Nonlinear EquationsReceived 30 November 2001; published 30 May 2002 Several nonlinear systems such as the Korteweg–de Vries (KdV) and modified KdV equations and λφ4 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. © 2002 The American Physical Society URL:
http://link.aps.org/doi/10.1103/PhysRevLett.88.244101
DOI:
10.1103/PhysRevLett.88.244101
PACS:
05.45.Yv, 02.30.Gp, 02.30.Jr
See AlsoComment: M. Jaworski and M. Lakshmanan, Comment on “Linear Superposition in Nonlinear Equations”, Phys. Rev. Lett. 90, 239401 (2003). Reply: A. Khare and U. Sukhatme, Khare and Sukhatme Reply, Phys. Rev. Lett. 90, 239402 (2003). |
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