Publication: The discretized Boussinesq equation and its conditional symmetry reduction
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2020-01-31
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IOP Publishing Ltd
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Abstract
In this article we show that we can carry out the symmetry preserving discretization of the Boussinesq equation with respect to three of its more significant conditional symmetries. We perform the symmetry reduction of the obtained nonlinear discrete schemes with respect to the conditional symmetries and obtain the reduced discrete equations which unlike in the continuous case, are not always reducible to second order difference equations. A numerical comparison with the exact continuous solution given by Weierstrass elliptic functions is carried out.
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© 2020 IOP Publishing Ltd.
DL has been supported by INFN IS-CSN4 Mathematical Methods of Nonlinear Physics. DL thanks the Departamento de Fisica Teorica of Universidad Complutense de Madrid (Spain) and the Department of Mathematics and Physics, Roma Tre University (Italy) for their hospitality. MAR was supported by the Spanish MINECO under project PGC2018-094898-B-I00 and thanks the INFN Sezione Roma Tre (Italy) for its hospitality. DL and ZT also thanks the hospitality of CRM, Montreal (Canada).