Multi-pulse edge-localized states on quantum graphs

We construct the edge-localized stationary states of nonlinear Schrödinger equation on a general quantum graph in limit large mass. Compared to previous works, we include arbitrary multi-pulse positive which approach asymptotically composition N solitons, each sitting bounded (pendant, looping, or internal) edge. give sufficient conditions edge lengths under such exist In addition, compute precise Morse index (the number negative eigenvalues corresponding linearized operator) for these states. If solitons state reside pendant and looping edges, prove that is exactly N. The technical novelty this work achieved by avoiding elliptic functions (and related exponentially small scalings) closing existence arguments terms Dirichlet-to-Neumann maps relevant parts given graph. illustrate results with three examples flower, dumbbell, single-interval graphs.