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| In this work we establish conditions for a class of third order partial differential equations to be strictly self-adjoint. Then, from a strictly self-adjoint subclass we consider those equations that admit a certain scaling symmetry. Thus we obtain a strictly self-adjoint and scaling invariant family of equations which includes the Benjamin-Bona-Mahony, Camassa-Holm and Novikov equations, and finally construct conservation laws for them using Ibragimov's conservation theorem. |
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