Variational principles for some nonlinear partial differential equations with variable coefficients

摘要

Variational principles for generalized Korteweg de Vries equation and nonlinear Schrodinger'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. (C) 2003 Elsevier Ltd. All rights reserved.