In this paper, a class of systems of three coupled real scalar fields is considered and also the general form of the stability equation is constructed. In order to discuss the stability of system the equations of motion with factorization method are solved. With the help of associated Jacobi differential equation the normal mode fluctuation is obtained .

Lagrangian systems described by coupled scalar fields are gaining renewed attention recently, and also the coupled scalar fields play an important role in supersymmetry. In supersymmetry, the solution of the solitonic field equations can be categorized by the topological defects as BPS and non-BPS states (Bogomol’nyi, 1967; and Prasad and Sommerfield, 1975).

In the case of two real scalar fields, the specific class of systems presented in literature (Bazeia et al., 1995; Bazeia and dos Santos, 1996; Bazeia et al., 1996a and 1996b) solved the corresponding equations of motion by field configurations, which are obeyed by the first order differential equations. General way for investigating stability was presented where in one has to know the spectrum of the corresponding Schrödinger operator (Jackiw, 1977; Rajaraman, 1979; Bazeia et al., 1995; Bazeia and dos Santos, 1996; Bazeia et al., 1996a and 1996b) Jackiw, 1977; and Bazeia et al., 1996b). In this paper we are going to discuss the three coupled scalar fields. The applications of three coupled scalar fields for hexagonal network defect are presented by Morris and Bazeia (1996); Bazeia and Brito (2000); Carroll et al. (2000); and Bazeia et al. (2002) and one scalar field with the domain walls is discussed by Bazeia et al., (2002). Also the three fields solutions in the Einstein equations for describing black holes with the cosmic strings are discussed by Frolov and Fursaev (2002). In general, these give us motivation to study three scalar fields. However, to make the present investigation as general as possible, we have organized the present work in the following manner—the class of systems of three coupled real scalar fields are presented and the topological profile of the classical configurations is discussed.

Factorization Method for Three Scalar Fields and BPS Bounds,Bazeia, coupled, scalar, presented, equations, stability, configurations, discuss, Santos, supersymmetry, associated, fluctuation, gaining, investigation, Lagrangian, motivation, operator, applications, renewed, Schrödinger, solitonic, Sommerfield, Carroll, categorized, topological