The Korteweg de Vries equation describes the evolution of surface elevation of low amplitude waves in...

 

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The Korteweg de Vries equation describes the evolution of surface elevation of low amplitude waves in time and (1-d) space. It reads: + gh hgh 3 9 + + Y 6 2 2h = 0 where g is the gravitational acceleration and h is the depth of the water layer. Non-dimensionalise the model and determine the characteristics scales coefficients that lead to the equation 10y + t + : 6 3 6 y 1 + = 0. (Note: to get to the equation above, besides t* and *, you have to choose y* as well.) The Korteweg de Vries equation describes the evolution of surface elevation of low amplitude waves in time and (1-d) space. It reads: + gh hgh 3 9 + + Y 6 2 2h = 0 where g is the gravitational acceleration and h is the depth of the water layer. Non-dimensionalise the model and determine the characteristics scales coefficients that lead to the equation 10y + t + : 6 3 6 y 1 + = 0. (Note: to get to the equation above, besides t* and *, you have to choose y* as well.)