Burgers equation on networks: Metric graph based approach
K. K. SabirovUniversity of Tashkent for Applied Sciences , 1 Gavkhar street , 100149 Tashkent , UzbekistanKhikmatjon MatyokubovD. U. MatrasulovTashkent University of Architecture and Civil Engineering , Yangishahar Str. 9A , 100095 Tashkent , Uzbekistan
2025en
ABI
Annotatsiya
Weconsider Burgers equation on metric graphs for simplest topologies such as star, loops, and tree graphs. Exact traveling wave solutions are obtained for the vertex boundary conditions providing mass conservation and continuity of the solution at the nodes. Constraints for the nonlinearity coefficients ensuring integrability of the Burgers equation are derived. Numerical treatment of the soliton dynamics and their transmission through the graph vertex is presented.
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