Part 1 in our series on Quantum Field Theory. Paul Dirac’s insights into the nature of Quantum Mechanics laid the foundation for Quantum Field Theory and predicted the existence of anti-matter. Part 1 ...

Stochastic nonlinear wave equations and Schrödinger equations represent a fascinating confluence of probability theory and the analysis of partial differential equations. By incorporating random ...

Quarterly of Applied Mathematics, Vol. 68, No. 1 (March 2010), pp. 61-71 (11 pages) We address the problem of describing solutions of the nonlinear Schrödinger equation on a compact surface in the ...

Physicists’ main goal is to be able to predict what will happen in the future based on patterns they’ve already observed, whether in massive systems of stars or tiny groups of atoms. Predicting ...

The heart of quantum mechanics is the wave-particle duality: matter and light possess both wave-like and particle-like attributes. Typically, the wave-like properties are inferred indirectly from the ...

We consider the system linearly coupled by nonlinear Schrödinger equations in ℝ3: $\{\begin{array}{c}-\mathrm{\Delta }{\mathrm{u}}_{\mathrm{j}}+{\mathrm{u ...