In this paper, we show the applicability of the first integral method for obtaining exact solutions of some nonlinear partial differential equations. By using this method, we found some exact solutions of the Landau-Ginburg-Higgs equation and generalized form of the nonlinear Schrödinger equation and approximate long water wave equations. The first integral method is a direct algebraic method for obtaining exact solutions of nonlinear partial differential equations. This method can be applied to nonintegrable equations as well as to integrable ones. This method is based on the theory of commutative algebra.
Taghizadeh, N.; Mirzazadeh, M.; and Paghaleh, A. S.
The First Integral Method to Nonlinear Partial Differential Equations,
Applications and Applied Mathematics: An International Journal (AAM), Vol. 7,
1, Article 7.
Available at: https://digitalcommons.pvamu.edu/aam/vol7/iss1/7