The generalized Fubini instanton

We show that (1+2)(1+2) nonlinear Klein–Gordon equation with negative coupling admits an exact solution which appears to be the linear superposition of the plane wave and the nonsingular rational soliton. We show that the same approach allows to construct the solution of similar properties for the Euclidean ϕ4ϕ4 model with broken symmetry. Interestingly, this regular solution will be of instanton type only in the D⩽5D⩽5 Euclidean space. Thus one can use the generalized Fubini instantons (in quantum cosmology for example) only for the case of the single infinite extra dimension.