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Recently, a lot of attention has been focused on the studies of the system
of nonlinear ordinary differential equation. A wide class of stochastic and
deterministic problems in physics, engineering and the other sciences are
modeled mathematically by differential equation as linear and nonlinear
differential equation, fractional differential equation, stochastic differential and
integro-differential equations system (Atanackovic and Stankovic, 2004;
Jafari and Daftardar-Gejji, 2006-08; Abulwafa et
al., 2006; and Amani and Sadeghi, 2007). The topological defects play an important role in cosmology and
particle physics. Topological defects and also the defect structures can be described
in (1,1) space-time dimension by different fields. These fields give us the
special potential which makes the nonlinear differential equation, and the solutions
of the corresponding equation are kinks or lumps. We note that two coupled
real scalar fields systems are good candidates for describing kink and lump
solution. The defect structures solution by orbit method are given in
Moris and Bazeia, 1996; Bazia and Brito, 2000; Carroll et al., 2000; and Bazia et al., 2002.
The application of the Homotopy Perturbation Method (HPM)
(He, 2004a;
He, 2005; and Jafari and Shaher Momani, 2007) is devoted to scientists
and engineers, because this method continuously deforms difficult problems
which becomes easier to solve. The HPM (He, 1999), was first proposed by He
(1998) and was further developed by (He, 1998, 2000, 2003 and 2004b). Very
recently some fruitful results have been obtained by HPM for solving various
nonlinear problems (Arief et al., 2006; Zhang and He, 2006; and Ganji and Sadighi, 2007).
Soliton solutions play an important role in different branches of physics.
They are found in equations of motion, a dynamical system that contains
nonlinear equations. In this paper, we investigate dynamical systems of
coupled scalar fields that are represented in the quantum field theory. |
