2018/11/14 by Eduard Kirr, Vivek Natarajan, Kirr, Eduard +1 · 1 citation
Mathematics · Physics and Astronomy · #35J61 #35Q55 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Photonic Systems #Nonlinear Waves and Solitons #Numerical methods for differential equations #Quantum Mechanics and Non-Hermitian Physics
paper · pdf · doi:10.48550/arxiv.1811.05716
openalex publication_date 2018/11/14 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper, we propose a method of finding all coherent structures\nsupported by a given nonlinear wave equation. It relies on enhancing the recent\nglobal bifurcation theory as developed by Dancer, Toland, Buffoni and others,\nby determining all the limit points of the coherent structure manifolds at the\nboundary of the Fredholm domain. Local bifurcation theory is then used to trace\nback these manifolds from their limit points into the interior of the Fredholm\ndomain identifying the singularities along them. This way all coherent\nstructure manifold are discovered except may be the ones which form loops and\nhence never reach the boundary. The method is then applied to the Schrodinger\nequation with a power nonlinearity for which all ground states are identified.\n