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The Lagrangian, Self‐Adjointness, and Conserved Quantities for a Generalized Regularized Long‐Wave Equation

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  • Long Wei
  • Yang Wang

Abstract

We consider the Lagrangian and the self‐adjointness of a generalized regularized long‐wave equation and its transformed equation. We show that the third‐order equation has a nonlocal Lagrangian with an auxiliary function and is strictly self‐adjoint; its transformed equation is nonlinearly self‐adjoint and the minimal order of the differential substitution is equal to one. Then by Ibragimov’s theorem on conservation laws we obtain some conserved qualities of the generalized regularized long‐wave equation.

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Handle: RePEc:wly:jnlaaa:v:2014:y:2014:i:1:n:173192
DOI: 10.1155/2014/173192
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