Quasi-Exact Solutions of the Equation for Description of Nonlinear Waves in a Liquid with Gas Bubbles

Existence results for the Kudryashov–Sinelshchikov–Olver equation

“…(1.1) was also derived for water waves by Olver [32] (see also [24]), using Hamiltonian perturbation theory, with further generalization given by Craig and Groves [16]. Mathematical properties of (1.1) were studied recently in many detail, including the existence of the travelling wave solutions [5,17,29,31,34,35,37,43], the solitary and periodic wave solutions [21,23], the periodic loop solutions [22], the soliton solutions [46], the quasi-exact solutions [25]. Methods to find exact solutions are in [1-3, 18-20, 30, 36, 38, 42, 44, 45, 47, 48].…”