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New exact solutions of a generalised Boussinesq equation with damping term and a system of variant Boussinesq equations via double reduction theory |
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| Authors: | Justina Ebele Okeke Rivendra Narain Kesh Sathasiva Govinder |
| Affiliation: | School of mathematics, statistics and computer science, University of Kwazulu Natal, Durban, South Africa,School of mathematics, statistics and computer science, University of Kwazulu Natal, Durban, South Africa,School of mathematics, statistics and computer science, University of Kwazulu Natal, Durban, South Africa |
| Abstract: | The conservation laws of a generalised Boussinesq (GB) equation with damping term are derived via the partial Noether approach. The derived conserved vectors are adjusted to satisfy the divergence condition. We use the definition of the association of symmetries of partial differential equations with conservation laws and the relationship between symmetries and conservation laws to find a double reduction of the equation. As a result, several new exact solutions are obtained. A similar analysis is performed for a system of variant Boussinesq (VB) equations. |
| Keywords: | Double reduction theory conservation laws partial Noether approach Lie symmetry method associated symmetry. |
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