Reductions of PDEs to second order ODEs and symbolic computation

J. Ramírez, J.L. Romero and C. Muriel

Applied Mathematics and Computation, 2016, vol. 291, issue C, 122-136

Abstract: A new method to obtain second-order reductions for ordinary differential equations which are polynomial in the derivatives of the dependent variable is presented. The method is applied to obtain reductions and new solutions to several well-known equations of mathematical physics: a lubrication equation, a thin-film equation, the Zoomeron equation and a family of 5th−order partial differential equations which includes the Caudrey–Dodd–Gibbon–Sawada–Kotera, Kaup–Kupershmidt, Ito and Lax equations. Some pieces of computer algebra code to derive the reductions are also included.

Keywords: Polynomial ordinary differential equations; Second-order reductions; Exact solutions of partial differential equations (search for similar items in EconPapers)
Date: 2016
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Persistent link: https://EconPapers.repec.org/RePEc:eee:apmaco:v:291:y:2016:i:c:p:122-136

DOI: 10.1016/j.amc.2016.06.043

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