firstname.lastname@example.org schrieb: > > email@example.com schrieb: > > > > Dear Ronald, please can you solve this: > > du/dt + u du/dx = - m d^4x/dx^4 - i n d^2x/dx^2 > > with IC u(x,0) = sin (x). > > x = [ 0 , 2pi ]; m and n are coefficients << 1 ; i is the imaginary unit. > > > > For n = m = 0 , this is the simply Burgers equation not viscous, but in this particulary case, I don't know how solve! > > > > Please, I have 3 questions: > > > > 1) Someone can solve this Burgers equation? > > 2) What happens in the case of m << n ? > > 3) What happens in the case of n << m ? > > > > Thanks > > Who's Ronald? Anyway, d^4x/dx^4 = 0 and d^2x/dx^2 = 0, no doubt. You > probably mean d^4u/dx^4 and d^2u/dx^2, don't you? >
The lack of response made me look into the reference:
This points to an August 14, 1996 (!) post by Ronald H. Brady starting a thread "Solution of Non-Linear PDE". He announces a solution of du/dt + u du/dx = 0 by means of series expansion.