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Compact structures as true non-linear phenomena

Emilio N. M. Cirillo Giuseppe Saccomandi Giulio Sciarra

*Corresponding author: Giuseppe Saccomandi giuseppe.saccomandi@unipg.it

MinE2019,3,434doi:10.3934/mine.2019.3.434

Traveling waves of permanent form with compact support are possible in several nonlinear partial nonlinear differential equations and this, mainly, along two pathways: A pure nonlinearity stronger than quadratic in the higher order gradient terms describing the mathematical model of the phenomena or a special inhomogeneity in quadratic gradient terms of the model. In the present note we perform a rigorous analysis of the mathematical structure of compactification via a generalization of a classical theorem by Weierstrass. Our mathematical analysis allows to explain in a rigorous and complete way the presence of compact structures in nonlinear partial differential equations 1 + 1 dimensions.

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