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.

Compact structures as true non-linear phenomena / Cirillo, Emilio N. M.; Saccomandi, Giuseppe; Sciarra, Giulio. - In: MATHEMATICS IN ENGINEERING. - ISSN 2640-3501. - (2019), pp. 434-446.

Compact structures as true non-linear phenomena

Emilio N. M. Cirillo;Giulio Sciarra
2019

Abstract

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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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1307066
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