Abstract
The study of shallow water waves, in (1+1)-dimensions, governed by the Korteweg-de Vries (KdV) equation, with logarithmic-law nonlinearity, is conducted in this paper. Exact Gaussian solitary wave solutions are obtained using three integration schemes. The conservation laws are listed. The adiabatic parameter dynamics is also given in presence of perturbation terms. The study is subsequently extended to (2+1)-dimensions where the Kadomtsev-Petviashvili (KP) equation, with log-law non linearity, is integrated. Finally; we consider two-layered shallow water waves modeled by coupled KdV equations.