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Infinitely narrow soliton solutions to systems of conservation laws. (English) Zbl 1014.35059
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.

35L65 Hyperbolic conservation laws
35Q51 Soliton equations
35L67 Shocks and singularities for hyperbolic equations
46F30 Generalized functions for nonlinear analysis (Rosinger, Colombeau, nonstandard, etc.)
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