A remark on a perturbed Benjamin-Bona-Mahony type equation and its complete integrability - Vovk, Myroslava I; Pukach, Petro Ya; Prykarpatski, Anatolij K (Annals of Mathematics and Physics, 2023)
In the Letter, we study a perturbed Benjamin-Bona-Mahony nonlinear equation, which was derived for describing shallow water waves and possessing a rich Lie symmetry structure. Based on the gradient-holonomic integrability checking scheme applied to this equation, we have analytically constructed its infinite hierarchy of conservation laws, derived two compatible Poisson structure and stated its complete integrability.