2025/04/16 by K. K. Sabirov, Sabirov, K. K., Kh. Sh. Matyokubov +3
Physics and Astronomy · Mathematics · #Nonlinear Waves and Solitons #Nonlinear Photonic Systems #Numerical methods for differential equations
paper · pdf · doi:10.48550/arxiv.2504.12232
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.