N-Soliton and Other Analytic Solutions for a (\(3 + 1\))-Dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff Equation with the Time-Dependent Coefficients for the Shallow Water Waves

Shallow water waves are seen in magnetohydrodynamics, atmospheric science, oceanography and so on. In this article, we study a ( \(3+1\) $3+1$ )-dimensional Korteweg–de Vries–Calogero–Bogoyavlenskii–Schiff equation with the time-dependent coefficients for the shallow water waves. N-soliton solutions are obtained via the simplified Hirota method. Via the N-soliton solutions, we present the elastic interactions between the two solitons and among the three solitons. Some other analytic solutions are constructed through the tanh method and \((\frac{G'}{G^{2}})\) $(\frac{G^{\prime }}{G^2})$ -expansion method.