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The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant
The Initial Boundary Problem For The Korteweg-De Vries Equation On The Negative Quarter-Plane, Prof. Tim Marchant
Tim Marchant
The initial boundary-value problem for the Korteweg-de Vries (KdV) equation on the negative quarter-plane, x < 0 and t > 0, is considered. The formulation of this problem is different to the usual initial boundary-value problem on the positive quarter-plane, for which x > 0 and t > 0. Two boundary conditions are required at x = 0 for the negative quarter-plane problem, in contrast to the one boundary condition needed at x = 0 for the positive quarter-plane problem. Solutions of the KdV equation on the infinite line, such as the soliton, cnoidal wave, mean height variation and undular bore solution, are used to find approximate …