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The goal of this study is to construct a novel family of travelling wave solutions for the system of (1 + 1)-coupled Konno-Oono equations (CKOEs). It occurs in optical nonlinear media, electromagnetic fields, plasma physics, and quantum fields. The invariant property of Lie symmetry analysis is exploited to extract analytical solutions. Lie symmetry analysis provides new similarity solutions for the system. A new variety of eighteen analytical solutions are compared to the reported results and the authors’ recently published work. In the previous results, a specific form of CKOEs with only two components, u and v, was solved in almost all cases, whereas in this study, a family of solutions was attained for three variables, u, v, and w. Solution profiles are portrayed via numerical simulation in order to make the solutions physically relevant.

The (2+1)-dimensional Gardner-Kadomtsov-Petviashvili (GKP) is an internal shallow water wave. Optimal subalgebra and invariants for the GKP are generated with the help of Killing form. This process yield some more explicit solutions of (2+1)-dimensional GKP by using similarity reduction via Lie-group theory. The solutions so obtained are different from the existing literature (

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