Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition

Details Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition

2002-03-12

arxiv.org/abs/nlin/0203018v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

19 pages, 4 figures

Scientific paper

10.1088/0305-4470/35/47/309

We show that a type of linear superposition principle works for several nonlinear differential equations. Using this approach, we find periodic solutions of the Kadomtsev-Petviashvili (KP) equation, the nonlinear Schrodinger (NLS) equation, the $\lambda \phi^4$ model, the sine-Gordon equation and the Boussinesq equation by making appropriate linear superpositions of known periodic solutions. This unusual procedure for generating solutions is successful as a consequence of some powerful, recently discovered, cyclic identities satisfied by the Jacobi elliptic functions.

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