# zbMATH — the first resource for mathematics

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.)
Full Text: