Finding general and explicit solutions of high nonlinear equations by the Exp-Function method.
Computers & Mathematics with Applications 01/2009; 58:2124-2130. pp.2124-2130
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ABSTRACT: It is shown that the solution produced by the Exp-function method may not hold for all ini-tial conditions. Riccati and Maccari nonlinear differential equations are used to illustrate that fact. Conditions of existence for the produced solution in the space of initial conditions and in the space of system's parameters are derived using the operator method based on the generalized operator of differentiation. The concept of the expansion of an ordinary dif-ferential equation is introduced and it is shown that the algebraic–analytical solution of Maccari equation can be produced by solving Riccati equation.Communications in Nonlinear Science and Numerical Simulation 02/2010; 15:3874-3886. · 2.81 Impact Factor
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