Titlebook: Scaling Limits and Models in Physical Processes; Carlo Cercignani,David H. Sattinger Book 1998 Springer Basel AG 1998 Applied mathematics.

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Scaling Limits and Models in Physical Processes978-3-0348-8810-3Series ISSN 1661-237X Series E-ISSN 2296-5041

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1661-237X Overview: 978-3-7643-5985-0978-3-0348-8810-3Series ISSN 1661-237X Series E-ISSN 2296-5041

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https://doi.org/10.1007/978-3-0348-8810-3Applied mathematics; Derivation; Finite; Invariant; equation; inverse scattering theory; mathematics; physi

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Inverse Scattering Theory Consider the eigenvalue problem for the Schrödinger equation.where . is real and lies in .(ℝ) is the class of all .∞ functions on the real line for which.for all non-negative integers . and .. It follows that all derivatives of . tend to zero as . → ±∞ faster than any power of .. Such functions are said to be rapidly decreasing.

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The Korteweg-de Vries Equation integrable. Moreover, the equation models some of the phenomena found in more complicated systems of nonlinear partial differential equations, such as the Euler equations for waves on the surface of an inviscid, irrotational fluid.

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