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Journal of Applied Nonlinear Dynamics 14(1) (2025) 163--174 | DOI:10.5890/JAND.2025.03.011

B. Gwaxa$^1$, Sameerah Jamal$^{1,2}$, A.G. Johnpillai$^3$

$^1$ School of Mathematics, University of the Witwatersrand, Johannesburg, South Africa

$^2$ DSI-NRF Centre of Excellence in Mathematical and Statistical Sciences (CoE-MaSS), South Africa

$^3$ Department of Mathematics, Eastern University, Sri Lanka, Chenkalady, 30350, Sri Lanka

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Abstract

In the present paper, we consider a special family of equations that are known to incorporate important wave features in oceanography studies. Physically, these equations admit generalized symmetries and non constant separants which implies they are of great relevance to integrability studies. These equations, are highly nonlinear and once reduced, are not solvable by conventional techniques. We construct series to effectively solve these evolution equations wherein recurrence relations occur and the convergence may be tested. Moreover, the conserved vectors of the equations are established.

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