Hirota, "Exact N-soliton solutions of the wave equation of long waves in shallow water and in nonlinear lattices," Journal of

Mathematical Physics, vol.

Subject public contracts awarded in the DNS will be under commercial conditions specified by Sponsor delivery software for analysis,

mathematical physics calculations, simulation and modeling.

Increasing attention is being paid to their legacy for its impact on many other fields of mathematics including algebraic geometry, dynamical systems, geometric group theory, number theory,

mathematical physics, and topology.

"How to design a language for

mathematical physics?" Hestenes asks.

Structures that exhibit a mix of deterministic and chaotic properties, for example, quasi-crystals, naturally arise in problems of geometry and

mathematical physics. Despite intense study, key questions about these structures remain wide open.The proposed research is an investigation of intermediate chaos in ergodic theory of dynamical systems.

The major themes addressed are hyperbolic geometry, automorphic functions, and applications to number theory; ordinary differential equations and dynamical systems; celestial mechanics and related problems; functions of several complex variables; algebraic topology and the Poincare conjecture; partial differential equations of

mathematical physics; probability; continuous groups (Lie groups) and their algebras; the principle of relativity and the Poincare group; applied physics; and the philosophy of science.

Objective: This project sets forth cutting-edge challenges in the field of

Mathematical Physics that will be solved within a common framework by making novel use of classical tools of Harmonic Analysis such as Oscillatory Integrals and Trigonometric Sums, the Cauchy operator, and the so-called Carleman estimates.

Knowledge of the fundamentals of classical mechanics and electromagnetism, introductory modern physics, and

mathematical physics is assumed.

The proposal studies problems concerning the geometry and topology of moduli spaces of Higgs bundles on a Riemann surface motivated by parallel considerations in number theory and

mathematical physics. In this way the proposal bridges various duality theories in string theory with the Langlands program in number theory.

Blow-Up in Nonlinear Equations of

Mathematical Physics: Theory and Methods

of Louisville and Perm State U., Russia) and Kyle Forinash (Indiana State U.) and programmer Tatyana Belozerova (Perm State U.) address the main topics of many courses in

mathematical physics within the fields of engineering, physics, mathematics, and applied mathematics.

Most introductions to

mathematical physics explain a theory than demonstrate it with examples and exercises, say Raine and his colleagues, but they reverse the order, using examples to introduce theory.