We sketch some of the different roles played by Whitham times in connection with averaging, adiabatic invariants, soliton theory, Hamiltonian structures, topological field theory (TFT), Seiberg-Witten (SW) theory, isomonodromy problems, Hitchin systems, WDVV and PicardFuchs equations, renormalization, soft supersymmetry breaking, etc.

In this paper, we apply and compare modified Variational Iteration Methods (VIMAP) to find travelling wave solutions of Whitham-Broer-Kaup (WBK) equations. The proposed modifications are made by introducing Adomian’s and He’s polynomials in the correction functional of the VIM. The use of Lagrange multiplier coupled with He’s polynomials explicitly reveal a clear edge over the coupling with Ado...

In a brief review, we discuss interrelations between arbitrary solutions of the loop equations that describe Hermitean one-matrix model and particular (multi-cut) solutions that describe concrete matrix integrals. These latter ones enjoy a series of specific properties and, in particular, are described in terms of Seiberg-Witten-Whitham theory. The simplest example of ordinary integral is consi...

The classical Lighthill-Whitham-Richards (LWR) kinematic traffic model is extended to a unidirectional road on which the maximum density a(x) represents road inhomogeneities, such as variable numbers of lanes, and is allowed to vary discontinuously. The car density φ = φ(x, t) is then determined by the following initial value problem for a scalar conservation law with a spatially discontinuous ...

Samantha K. Chapman ([email protected]), Smithsonian Environmental Research Center, Edgewater, MD 21037, USA. Jennifer A. Schweitzer, School of Forestry, Northern Arizona Univ., Flagstaff, AZ 86011, USA. Present address: Dept. of Ecology and Evolutionary Biology, Univ. of Tennessee, TE, USA. Thomas G. Whitham, Merriam Powell Center for Environmental Research, Flagstaff, AZ 86011, USA and Dept of ...

This brief review deals with prepotentials inspired by N = 1 SUSY considerations due to Cachazo, Intrilligator, Vafa. These prepotentials associated with matrix models following Dijkgraaf and Vafa should be considered as given on an enlarged moduli space that includes Whitham times (couplings of the superpotential). This moduli space is nothing but the whole moduli space of (decorated) hyperell...

This paper is a preliminary study of a simple method to construct semihamiltonian systems starting from a flat bidifferential ideal. The method is based on a suitable interpretation of a transformation used by different authors to compute the symmetries of the Whitham equations.