Bifurcation diagrams of coupled Schrödinger equations

Radially symmetric solutions of many important systems of partial differential equations can be reduced to systems of special ordinary differential equations. A numerical solver for initial value problems for such systems is developed based on Matlab, and numerical bifurcation diagrams are obtained according to the behavior of the solutions. Various bifurcation diagrams of coupled Schrödinger equations from nonlinear physics are obtained, which suggests the uniqueness of the ground state solution.