An indirect variable transformation approach and Jacobi elliptic solutions to Korteweg de Vries equation

Based on a variable change and the variable separated ODE method, an indirect variable transformation approach is proposed to search exact solutions to special types of partial differential equations (PDEs). The new method provides a more systematical and convenient handling of the solution process for the nonlinear equations. Its key point is to reduce the given PDEs to variable-coefficient ordinary differential equations, then we look for solutions to the resulting equations by some methods. As an application, exact solutions for the KdV equation are formally derived.