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Boundary value problems for discrete and continuous nonlinear Schrödinger equations
It is well known that the Fourier transform can be used to solve initial value problems (IVPs) for linear partial differential equations (PDEs). It is also well known that a special class of nonlinear PDEs exists for which ...
Lyapunov-Schmidt reduction and bifurcation analysis for boundary value problems inspired by classical stability problems
Theoretic and numerical methods applied on the Lyapunov-Schmidt reduced bifurcation equation for boundary value problems such as the planar Benard problem with periodic boundary on the cubic. The main results of my research ...