Nonlinear Sciences > Exactly Solvable and Integrable Systems
[Submitted on 16 Apr 2025
]
Title: Burgers equation on networks: Metric graph based approach
Title: 网络上的 Burgers 方程：基于度量图的方法
Abstract: 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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