An extended hadron model based on the exact solution of the nonlinear field equation

An extended hadron model is presented. This is based on two exact analytic solutions of two field equations in one space dimension: One is for the nonlinear field equation on the neutral scalar field for the polynomial potential V(phi)=lambda2(phi2+α2)2(phi2-β2)2 and the other is for the quark field equation with interaction to the neutral scalar field. Our potential has three local minimums: Two of them are absolute minimums and are for the vacuum state and the other is a slightly high local minimum and is for the hadron state. The stability of our exact solutions is proved. Our model leads to the conclusion that the quarks are forced to be confined within the wall of the neutral scalar field. This explains the quark confinement clearly. Hence our model gives the field theoretical realization of the MIT bag model. (auth.)