A modified F-expansion method to find the exact traveling wave solutions of  two-component nonlinear partial differential equations (NLPDEs) is discussed. We use this method to construct many new solutions to the nonlinear Whitham-Broer-Kaup system (1+1)-dimensional. The solutions obtained include Jacobi elliptic periodic wave solutions which exactly degenerate to the soliton solutions, triangu...

AIMÉE T. CLASSEN*†‡, SAMANTHA K. CHAPMAN*§, THOMAS G. WHITHAM*, STEPHEN C. HART¶ and GEORGE W. KOCH* * Department of Biological Sciences, Northern Arizona University, Flagstaff, AZ 86011, † Environmental Sciences Division, Oak Ridge National Laboratory, Oak Ridge, TN 37831–6422, ‡ Ecology and Evolutionary Biology Department, The University of Tennessee, Knoxville, TN 37996, § Smithsonian Enviro...

In order to model the impact of incidents an alternative resolution method is proposed for the Lighthill-Whitham-Richards model. Is is based on an explicit handling of shock waves (generation, tracking and collision). Contrary to finite difference methods which impose a fixed discretization grid, the Wave Tracking method is event based. The different possible events are studied and they all lea...

The Riemann-Hilbert problems for multiple orthogonal polynomials of types I and II are used to derive string equations associated to pairs of Lax-Orlov operators. A method for determining the quasiclassical limit of string equations in the phase space of the Whitham hierarchy of dispersionless integrable systems is provided. Applications to the analysis of the large-n limit of multiple orthogon...

In this paper, based on the known first integral method, we try to seek the traveling wave solutions of several nonlinear evolution equations. As a result, some exact travelig wave solutions and solitary solutions for Whitham-Broer-Kaup (WBK) equations, Gardner equation, Boussinesq-Burgers equations, nonlinear schrodinger equation and mKDV equation are established successfully. Key–Words: First...

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...

We prove the existence of highest, cusped, periodic travelling-wave solutions with exact and optimal $ \alpha $-H\"older continuity in a class fractional negative-order dispersive equations form \begin{equation*} u_t + (| \mathrm{D} |^{- \alpha} u n(u) )_x = 0 \end{equation*} for every \in (0, 1) homogeneous Fourier multiplier | |^{ - $. tackle nonlinearities type |^p or |^{p 1} all real p > 1 ...