Numerical Methods for the Benjamin-Ono Equation
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In this thesis, we compare four numerical methods for solving the Benjamin-Ono equation. The numerical methods are presented in detail, and we compare them for different test problems. We derive the Hirota bilinear form of the Benjamin-Ono equation, and present spatially periodic exact solutions. The best numerical method is Chan and Kerkhoven's Semi-Implicit Fourier pseudospectral method, originally intended for the Korteweg-de Vries equation. In the last chapter, we study the zero dispersion limit for the Korteweg-de Vries and Benjamin-Ono equation. We observe that the small dispersion term forces the shock formation in the solution to become travelling waves.