The Gould-Hopper Polynomials in the Novikov-Veselov equation

Abstract

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.

22 pages, no figure

References in corpus (5)

• Two-dimensional rational solitons and their blow-up via the Moutard transformation
• The Novikov-Veselov hierarchy of equations and integrable deformations of minimal Lagrangian tori in CP^2
• Abelian Chern-Simons Vortices and Holomorphic Burgers' Hierarchy
• New exact multi line soliton and periodic solutions with constant asymptotic values at infinity of the NVN integrable nonlinear evolution equation via dibar-dressing method
• New Reductions and Nonlinear Systems for 2D Schrodinger Operators

Cited by in corpus (2)

• Numerical study of blow-up and stability of line solitons for the Novikov-Veselov equation
• Quasi-invariant Hermite polynomials and Lassalle-Nekrasov correspondence