This paper primarily concerns the Whitham modulation equation of complex modified Korteweg–de Vries (cmKdV) with a step-like initial value. By utilizing Lax pair, we derive N-genus equations via averaging method. The can be integrated using hodograph transformation. We investigate Krichever’s algebro-geometric scheme to propose method for cmKdV integrable hierarchy and obtain velocities connect...

Genetic differentiation and heterozygosity in pinyon pine associated with herbivory and environmental stress. Evolution 45: 989–999. Okasha S. 2008. Evolution and the levels of selection. Oxford, UK: Oxford University Press. Parrent JL, Peay K, Arnold AE, Comas LH, Avis P, Tuininga A. 2010. Moving from pattern to process in fungal symbioses: linking functional traits, community ecology, and phy...

We introduce a new model of traffic flow with phase transitions. The model is obtained by coupling together the classical Lighthill-Whitham-Richards (LWR) equation with the 2 × 2 system described in [A. Aw and M. Rascle, Resurrection of “second order” models of traffic flow, SIAM J. Appl. Math., 60 (2000), pp. 916–938]. We describe the solutions of the Riemann problem, and we compare the result...

We review the Seiberg-Witten construction of low-energy effective actions and BPS spectra in SUSY gauge theories and its formulation in terms of integrable systems. It is also demonstrated how this formulation naturally appears from the compactified version of the theory with partially broken supersymmetry so that the integrable structures arise from the relation between bare and quantum variab...

We consider hydrodynamic systems which possess a local Hamiltonian structure of Dubrovin-Novikov type. To such a system there are also associated an infinite number of nonlocal Hamiltonian strctures of Mokhov-Ferapontov type. We give necessary and sufficient conditions so that, after a nonlinear transformation of the independent variables, the reciprocal system still possesses a local Hamiltoni...