Higher-Dimensional KdV Equations and Their Soliton Solutions

Abstract

A (2+1)-dimensional KdV equation is obtained by use of Hirota method, which possesses N -soliton solution, specially its exact two-soliton solution is presented. By employing a proper algebraic transformation and the Riccati equation, a type of bell-shape soliton solutions are produced via regarding the variable in the Riccati equation as the independent variable. Finally, we extend the above (2+1)-dimensional KdV equation into (3+1)-dimensional equation, the two-soliton solutions are given.