(2+1)-dimensional KdV, fifth-order KdV, and Gardner equations derived from the ideal fluid model. Soliton, cnoidal and superposition solutions

We study the problem of gravity surface waves for an ideal fluid model in (2+1)-dimensional case. apply a systematic procedure to derive Boussinesq equations given relation between orders four expansion parameters, amplitude parameter $\alpha$, long-wavelength $\beta$, transverse wavelength $\gamma$, and bottom variation $\delta$. derived only possible extensions Korteweg-de Vries equation, fifth-order KdV Gardner equation three special cases relationship these parameters. All are non-local. When is flat, can be transformed Kadomtsev-Petviashvili fixed reference frame next classical KP moving frame. have found soliton, cnoidal, superposition solutions (essentially one-dimensional) equation.