Higher-Dimensional KdV Equations and Their Soliton Solutions

A (2+1)-dimensional KdV equation is obtained by use of Hirotamethod, which possesses N-soliton solution, specially its exacttwo-soliton solution is presented. By employing a proper algebraictransformation and the Riccati equation, a type of bell-shapesoliton solutions are produced via regarding the variable in theRiccati equation as the independent variable. Finally, we extendthe above (2+1)-dimensional KdV equation into (3+1)-dimensionalequation, the two-soliton solutions are given.