| Abstract: |
| Rational solutions of the Painleve-IV equation constructed from generalized
Okamoto polymomials are used to build special families of solutions for a
variety of nonlinear wave equations, including the defocusing NLS equation,
the Boussinesq equation, and the dispersive water wave equation. The zeros
and poles of these Painleve-IV functions form remarkably regular rectangular
and triangular patterns in the complex plane. We formulate an associated
Riemann-Hilbert problem and use it to analyze the asymptotic behavior of these
rational Painleve-IV functions in the large-degree limit. |
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