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arXiv · 1701.04854

Conservation laws and symmetries of a generalized Kawahara equation

Maria Luz Gandarias·Maria Rosa·Elena Recio·Stephen C. Anco
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Abstract

The generalized Kawahara equation $u_t=a(t) u_{xxxxx} +b(t)u_{xxx} +c(t)f(u) u_x$ appears in many physical applications. A complete classification of low-order conservation laws and point symmetries is obtained for this equation, which includes as a special case the usual Kawahara equation $u_t = \alpha u u_x+\beta u^2u_x +\gamma u_{xxx}+\mu u_{xxxxx}$. A general connection between conservation laws and symmetries for the generalized Kawahara equation is derived through the Hamiltonian structure of this equation and its relationship to Noether's theorem using a potential formulation.

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Maria Luz Gandarias, Maria Rosa, Elena Recio, Stephen C. Anco. 2017-01-17. Conservation laws and symmetries of a generalized Kawahara equation. https://doi.org/10.1063/1.4982012

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