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Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition

Fred Cooper·Avinash Khare·Uday Sukhatme
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Abstract

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 $λϕ^4$ 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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Fred Cooper, Avinash Khare, Uday Sukhatme. 2002-06-07. Periodic Solutions of Nonlinear Equations Obtained by Linear Superposition. https://doi.org/10.1088/0305-4470%2F35%2F47%2F309

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