BRANCHING SOLUTIONS OF THE NON-LINEAR DIFFERTIAL EQUATIONS OF THE SECOND ORDER OF THE PHISIC

It is shown, that in case of the heterogeneous system, there are two types of phase transition of the second order, that corresponds to two types of accidents in such system. In the first case the length of the period of the periodic solution of the corresponding equation is constant and coincides with the length of a crystal grid of a system, in the second case the length of the period of the periodic decision is not a constant. In the first case in a point of accident (k121) parameter of the order η=0, in the second case η=(α0 /2β0 )0. In the first case, in a point of accident phase transition of the second-order takes place in the isolated points and in their environments, in the second case phase transition occurs in the whole system. Transition of the first type when in a point of phase transition η=0, is an analogue of phase transition of the second-order of L. D. Landau in case of homogeneous system. Transition of the second type, when in a point of phase transition η=(α0 /2β0 )0, is a new type of phase transition of the second-order. Phase transition of this type occurs in all system at the same time.

BRANCHING SOLUTIONS OF THE NON-LINEAR DIFFERTIAL EQUATIONS OF THE SECOND ORDER OF THE PHISI

It is shown, that in case of the heterogeneous system, there are two types of phase transition of the second order, that corresponds to two types of accidents in such system. In the first case the length of the period of the periodic solution of the corresponding equation is constant and coincides with the length of a crystal grid of a system, in the second case the length of the period of the periodic decision is not a constant. In the first case in a point of accident (k121) parameter of the order η=0, in the second case η=(α0 /2β0 )0. In the first case, in a point of accident phase transition of the second-order takes place in the isolated points and in their environments, in the second case phase transition occurs in the whole system. Transition of the first type when in a point of phase transition η=0, is an analogue of phase transition of the second-order of L. D. Landau in case of homogeneous system. Transition of the second type, when in a point of phase transition η=(α0 /2β0 )0, is a new type of phase transition of the second-order. Phase transition of this type occurs in all system at the same time.