Benjamin–Bona–Mahony (BBM) equation with variable coefficients: Similarity reductions and Painlevé analysis

Reductions and conservation laws for BBM and modified BBM equations

“…This equation can also characterize the hydro-magnetic wave in cold plasma, acoustic-gravity waves in compressible fluids and acoustic waves in an-harmonic crystals. Physical applications and mathematical properties of these equations have been discussed in other papers [3,4,7,10]. Khalique presented some result regarding BBM equation and we cover all of them [12].…”

“…Originally KdV derived to describe shallow water waves of long wavelength and small amplitude. BBM and KdV are useful for modelling surface waves of long wavelength in liquids, acoustic-gravity waves in compressible fluids, hydromagnetics waves in cold plasma and acoustic waves in anharmonic crystals [3,4,[7][8][9][10]. Peregrine also derived the BBM equations to regularized long-wave equation [11].…”

Solutions of Konopelchenko-Dubrovsky Equation by Traveling Wave Hypothesis and Lie Symmetry Approach

“…In this subsection, we apply Lie symmetry approach [11,12] to find symmetries and we obtain some exact solutions of equations (1) and (2).…”

Benjamin–Bona–Mahony Equation with Variable Coefficients: Conservation Laws

“…It is also known as the regularized long-wave equation and is applicable to shallow water waves and to the study of drift waves in plasma or the Rossby waves in rotating fluids. See, for example, [2] and references therein. It should be noted, however, that the BBM equation was also derived by Peregrine [3].…”

“…In the last two decades, various versions of the Benjamin-Bona-Mahony equation have been investigated in the literature. A general form of the Benjamin-Bona-Mahony equation is [2] u t + αu x + βuu x + δu xxt = 0…”