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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.

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.)
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