Abstract
In this study, three well-known partial differential equations (PDEs) are extended to their logarithmic nonlinearities with and without attenuation terms. These new models are the logarithmic unstable nonlinear Schrödinger (UNLS), the logarithmic Hamiltonian amplitude, and the logarithmic extended UNLS equations. As a result, the new logarithmic equations are investigated to find their Gaussian solitary waves (GSWs). The GSW solutions are presented for all new logarithmic models. Furthermore, we demonstrated that all logarithmic models are distinguishable by GSWs. These logarithmic extensions and their Gaussian solutions will be useful to find logarithmic extensions of other PDEs.
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