The Gould-Hopper Polynomials in the Novikov-Veselov equation

Details The Gould-Hopper Polynomials in the Novikov-Veselov equation The Gould-Hopper Polynomials in the Novikov-Veselov equation

2010-11-07

arxiv.org/abs/1011.1614v2

Nonlinear Sciences

Exactly Solvable and Integrable Systems

22 pages, no figure

Scientific paper

We use the Gould-Hopper (GH) polynomials to investigate the Novikov-Veselov (NV) equation. The root dynamics of the $\sigma$-flow in the NV equation is studied using the GH polynomials and then the Lax pair is found. In particulr, when $N=3,4,5$, one can get the Gold-fish model. The smooth rational solutions of the NV equation are also constructed via the extended Moutard transformation and the GH polynomials. The asymptotic behavior is discussed and then the smooth rational solution of the Liouville equation is obtained.

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