... Compatibility conditions Researchers performed powerful studies of integrable systems where useful findings were achieved. Studies on the propagation of many nonlinear structures in fluid mediums, in (1 + 1) dimensions and higher-dimensional media, have been remarkably flourishing in fluid dynamics...

... for u₁–u₅ were observed and we found that u₆ turns out to be an arbitrary function, and also compatibility conditions, for k = 6, is satisfied identically. This, in turn, confirms the Painlevė integrability of equation (4) . where, α...

... © Emerald Publishing Limited 2020 Emerald Publishing Limited Licensed re-use rights only Vakhnenko–Parkes equation Painlevé analysis Compatibility conditions Integrable systems in solitary waves theory are very attractive areas in nonlinear sciences. Nonlinear integrable...

... complex soliton solutions. Findings The two developed BLMP models exhibit complete integrability for any constant coefficient and any analytic time-dependent coefficients by investigating the compatibility conditions for each developed model. Research limitations/implications The paper presents...

..., u₄ and u₅, and we found that u₆ turns out to be an arbitrary function, and also, compatibility conditions, for k  =  6, are satisfied identically. Painlevé analysis Compatibility conditions Sakovich equation Compatibility conditions...

... analytic time-dependent coefficients defined though compatibility conditions. Research limitations/implications The paper presents an efficient algorithm for handling time-dependent integrable equations with analytic time-dependent coefficients. Practical implications This study introduces three...