Solitary wave solutions, periodic and superposition solutions to the system of first-order (2+1)-dimensional Boussinesq's equations derived from the Euler equations for an ideal fluid model

Abstract This article concludes the study of (2+1) -dimensional nonlinear wave equations that can be derived in a model of an ideal fluid with irrotational motion. In the considered case of identical scaling of the x, y variables, obtaining a (2+1) -dimensional wave equation analogous to the KdV equation is impossible. Instead, from a system of two first-order Boussinesq equations, a non-linear wave equation for the auxiliary function f (x, y, t) defining the velocity potential can be obtained, and only from its solutions can the surface wave form (x, y, t) be obtained. We demonstrate the existence of families of (2+1) -dimensional traveling wave solutions, including solitary and periodic solutions, of both cnoidal and superposition types. MSC Classification: 02. 30. Jr, 05. 45. -a, 47. 35. B, 47. 35. Fg