A Change in Wave Type Modeled by the Variable Coefficient Korteweg-deVries Equation

Abstract

Strongly shoaling solutions to the variable coefficient Korteweg-deVries equation have been obtained for arbitrary initial or off-shore waveforms and depth variations. Although the solutions were capable of exhibiting dispersive behavior off-shore, the near-shore behavior was always found to be governed by a variable coefficient Burger equation. Conditions under which the wave slope became infinite were given in terms of the initial shape of the wave and the depth variation. These solutions are valid when α < < δ < < 1, where α is the ratio of the initial wave amplitude to the depth and δ is the ratio of the initial length of the wave to the length scale associated with the depth variation. Numerical solutions of this equation were also found; these were in excellent agreement with the asymptotic results.