Solutions of the real dispersionless Veselov–Novikov hierarchy

J.-H. Chang, Yu.-T. Chen

National Defense University, Department of Electrical Engineering

Abstract: We investigate the dispersionless Veselov–Novikov (dVN) equation in the framework of the dispersionless two-component $B$KP hierarchy. We consider symmetry constraints for the real dVN system and show that the conserved densities are related to Faber polynomials and can be solved recursively. In addition, we use the Faber polynomials to find hodograph solutions of the dVN hierarchy.

Keywords: dVN hierarchy, Hirota equation, Faber polynomial, hodograph.

DOI: 10.4213/tmf6358

 English version: Theoretical and Mathematical Physics, 2009, 159:3, 741–751

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