Discontinuous traveling waves as weak solutions to the Fornberg-Whitham equation. (English) Zbl 1394.35099
Summary: We analyze the weak solution concept for the Fornberg-Whitham equation in case of traveling waves with a piecewise smooth profile function. The existence of discontinuous weak traveling wave solutions is shown by means of analysis of a corresponding planar dynamical system and appropriate patching of disconnected orbits.
MSC:
| 35C07 | Traveling wave solutions |
| 35R09 | Integro-partial differential equations |
| 35D30 | Weak solutions to PDEs |
| 35L67 | Shocks and singularities for hyperbolic equations |
Keywords:
nonlinear integro-differential equations; piecewise smooth profile function; patching of disconnected orbitsReferences:
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