(2+1)-Dimensional Fifth-Order KdV Equation and (2+1)-Dimensional Gardner Equation Obtained from Ideal Fluid Model Revisited—Solitary Wave Solutions

Abstract

The (2+1)-dimensional fifth-order KdV equation and (2+1)-dimensional Gardner equation obtained by us using Euler equations for an ideal fluid model in 2023 are revisited. Including additional second-order corrections enabled the derivation of the (2+1)-dimensional fifth-order KdV and Gardner equations without relying on the additional assumptions previously required. The new forms of these equations include an additional non-local term, which allows for the existence of families of solitary wave solutions analogous to solutions to those of the (1+1)-dimensional fifth-order KdV and Gardner equations.

Keywords

• (2+1)-dimensional fifth-order KdV equation
• (2+1)-dimensional Gardner equation
• solitary wave solutions
• ideal fluid model