In this letter, He’s Variational iteration method (VIM) is implemented for solving the nonlinear Whitham-Broer-Kaup partial differential equations. This method is based on Lagrange multipliers for identification of optimal values of parameters in a functional. Using this method creates a sequence which tends to the exact solution of the problem. The results are compared with those obtained by t...

In this paper, we employ the bifurcation method of dynamical systems to investigate the exact travelling wave solutions for the Fornberg-Whitham equation ut − uxxt + ux+uux = uuxxx+3uxuxx. The implicit expression for solitons is given. The explicit expressions for peakons and periodic cusp wave solutions are also obtained. Further, we show that the limits of soliton solutions and periodic cusp ...

SUMMARY This paper presents an extension of Lighthill, Whitham and Richards' dynamic traffic flow model (LWR) to a number of vehicle classes. Each class will be described by a separate fundamental diagram. When the various diagrams are similar in shape a scaling can be carried out that is related to the passenger-car equivalents. We present both an analytical framework and a numerical computati...

We suggest the brane interpretation of the integrable dynamics behind the exact solution to the N=2 SUSY YM theory.Degrees of freedom of the Calogero type integrable system responsible for the appearance of the spectral Riemann surfaces originate from degrees of freedom of the dynamical branes. The second integrable system of the Whitham type corresponds to the scattering of branes similar to t...

We consider an extension of the traffic flow model proposed by Lighthill, Whitham and Richards, in which the mean velocity depends on a weighted mean of the downstream traffic density. We prove well-posedness and a regularity result for entropy weak solutions of the corresponding Cauchy problem, and use a finite volume central scheme to compute approximate solutions. We perform numerical tests ...

I review the appearance of classical integrable systems as an effective tool for the description of nonperturbative exact results in quantum string and gauge theories. Various aspects of this relation: spectral curves, action-angle variables, Whitham deformations and associativity equations are considered separately demonstrating hidden parallels between topological 2d string theories and naive...

We review new aspects of integrable systems discovered recently in N = 2 supersymmetric gauge theories and their topologically twisted versions. The main topics are (i) an explicit construction of Whitham deformations of the Seiberg-Witten curves for classical gauge groups, (ii) its application to contact terms in the u-plane integral of topologically twisted theories, and (iii) a connection be...

The dispersionless Whitham modulation equations in one space dimension and time 4 are generically hyperbolic or elliptic, and breakdown at the transition, which is a curve in the 5 frequency-wavenumber plane. In this paper, the modulation theory is reformulated with a slow 6 phase and different scalings resulting in a phase modulation equation near the singular curves which 7 is a geometric for...