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.
"The Lagrangian, Self-Adjointness, and Conserved Quantities for a Generalized Regularized Long-Wave Equation." Abstr. Appl. Anal. 2014 1 - 5, 2014. https://doi.org/10.1155/2014/173192