Solutions for Some Mathematical Physics Problems Issued from Modeling Real Phenomena: Part 1

On some spectral problems of mathematical physics

The article contains a brief survey of some spectral problems of mathematical physics that have been arising recently in optics, mesoscopic systems, quantum chaos, and other areas. In particular, problems of photonic crystal theory, waveguides, and quantum graphs are addressed. This text is a modified version of the lectures delivered at the Pan-American Advanced Studies Institute (PASI) on Par...

Asymptotic Phenomena in Mathematical Physics

The problems I intend to speak about belong to the somewhat undefined and disputed region at the border between mathematics and physics. The fields of physics from which these problems originate are rather classical; the mathematical questions involved are also rather classical. That does not mean that these problems belong to the past. On the contrary, they are quite alive today and—I am convi...

Travelling wave solutions to some PDEs of mathematical physics

Nonlinear operations such as multiplication of distributions are not allowed in the classical theory of distributions. As a result, some ambiguities arise when we want to solve nonlinear partial differential equations such as differential equations of elasticity andmultifluid flows, or some new cosmological models such as signature changing space-times. Colombeau’s new theory of generalized fun...

Some Problems in the Theory of Dynamical Systems & Mathematical Physics *

Open problems in mathematical physics

We present a list of open questions in mathematical physics. After a historical introduction, a number of problems in a variety of different fields are discussed, with the intention of giving an overall impression of the current status of mathematical physics, particularly in the topical fields of classical general relativity, cosmology and the quantum realm. This list is motivated by the recen...