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Nonlinear self-adjointness of a generalized fifth-order KdV equation. (English) Zbl 1234.35221
Summary: The new concepts of self-adjoint equations formulated by N. H. Ibragimov [J. Math. Anal. Appl. 318, No. 2, 742–757 (2006; Zbl 1102.34002); J. Phys. A, Math. Theor. 44, No. 43, Article ID 432002, 8 p. (2011; Zbl 1270.35031)] and M. L. Gandarias [J. Phys. A, Math. Theor. 44, No. 26, Article ID 262001, 6 p. (2011; Zbl 1223.35203)] are applied to a class of fifth-order evolution equations. Then, from N. H. Ibragimov’s theorem on conservation laws [J. Math. Anal. Appl. 333, No. 1, 311–328 (2007; Zbl 1160.35008)], conservation laws for the generalized Kawahara equation, simplified Kahawara equation and modified simplified Kawahara equation are established.
MSC:
35Q53KdV-like (Korteweg-de Vries) equations
35L65Conservation laws
47B25Symmetric and selfadjoint operators (unbounded)
76M60Symmetry analysis, Lie group and algebra methods (fluid mechanics)