Construction of exact travelling waves for the Benjamin-Bona-Mahony equation on networks. (English) Zbl 1315.35052
This paper is concerned with the existence of traveling wave solutions of the Benjamin-Bona-Mahony equation for a finite metric tree with edges \(e_i\):
\[
u_t -a_i u_{xxt} +b_i uu_x +d_i u_x =0 \quad \text{on each } e_i,
\]
where Dirichlet boundary conditions are assumed at endpoints, and continuity conditions and Kirchhoff conditions are assumed at vertices \(e_i \cap e_j\). Under certain conditions, the authors establish the existence of traveling waves for the above system on networks.
Reviewer: Bixiang Wang (Socorro)
MSC:
35C07 | Traveling wave solutions |
35R02 | PDEs on graphs and networks (ramified or polygonal spaces) |
35K55 | Nonlinear parabolic equations |