Nedeljkov, Marko Infinitely narrow soliton solutions to systems of conservation laws. (English) Zbl 1014.35059 Novi Sad J. Math. 31, No. 2, 59-68 (2001). An infinitely narrow \(N\)-soliton, as a solution to a system of conservation laws is constructed and considered in an algebra of generalized functions where it makes sense. Then, with appropriate assumptions, it is shown that a modified solution is a classical solution to the system of conservation laws. The method used by the author is another useful interpretation of the so-called asymptotic method developed by Maslov and his pupils Omeljanov, Danilov and others developed here in the framework of Colombeau algebra of generalized functions. Reviewer: Stevan Pilipović (Novi Sad) Cited in 2 Documents MSC: 35L65 Hyperbolic conservation laws 35Q51 Soliton equations 35L67 Shocks and singularities for hyperbolic equations 46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.) Keywords:Colombeau algebra of generalized functions; generalized solutions PDFBibTeX XMLCite \textit{M. Nedeljkov}, Novi Sad J. Math. 31, No. 2, 59--68 (2001; Zbl 1014.35059) Full Text: EuDML