Periodic solutions of nonlinear equations obtained by linear superposition

DOI10.1088/0305-4470/35/47/309zbMATH Open1039.35098arXivnlin/0203018OpenAlexW2071326024MaRDI QIDQ4468212

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Publication date: 10 June 2004

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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

l a m b d a p h i^{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.

Full work available at URL: https://arxiv.org/abs/nlin/0203018

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