This paper is concerned with an extended \((3+1)\) -dimensional shallow water wave equation with variable coefficients, which is used to describe the interaction of nonlinear waves in ocean dynamics, shallow water waves, etc. Hereby, it is of further value to investigate the integrability characteristics of this model. Firstly, we conduct the Painlevé analysis and find it can pass the Painlevé test. Then, the one- and two-soliton solution are obtained by virtue of the Hirota bilinear method. Bäcklund transformation, Lax pair and infinitely many conservation laws are derived through the Hirota bilinear method and Bell polynomial approach. Particularly, we generate two type of interaction solutions in terms of a combination of quadratic function, exponential function and trigonometric function, namely, the lump-kink solution and the periodic lump solution. Finally, dynamics characteristics and evolution behaviors are exhibited for the obtained solution waves through particular plots with proper choices of different values for the parameters.
