| Article ID | Journal | Published Year | Pages | File Type |
|---|---|---|---|---|
| 758873 | Communications in Nonlinear Science and Numerical Simulation | 2014 | 6 Pages |
•Differential substitutions can provide new conservation laws.•The classes of nonlinearly self-adjoint Harry-Dym type equations and modified Harry-Dym equation are obtained.•Some conservation laws for these equations, associated to classical generators, are established.
It is known (Ibragimov, 2011; Galiakberova and Ibragimov, 2013) [14,18] that the property of nonlinear self-adjointness allows to associate conservation laws of the equations under study, with their symmetries. In this paper we show that, even when the equation is nonlinearly self-adjoint with a non differential substitution, finding the explicit form of the differential substitution can provide new conservation laws associated to its symmetries. By using the general theorem on conservation laws (Ibragimov, 2007) [11] and the property of nonlinear self-adjointness we find some new conservation laws for the modified Harry-Dym equation. By using a differential substitution we construct a conservation law for the Harry-Dym equation, which has not been derived before using Ibragimov method.
