Variational principles for some nonlinear partial differential equations with variable coefficients

Variational principles for generalized Korteweg–de Vries equation and nonlinear Schrödinger’s equation are obtained by the semi-inverse method. The most interesting features of the proposed method are its extreme simplicity and concise forms of variational functionals for a wide range of nonlinear problems. Comparison with the results obtained by the Noether’s theorem is made, revealing the present theorem is a straightforward and attracting mathematical tool.