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to find the exact solution of 1D Burges Equation

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Old   May 11, 2003, 05:17
Default to find the exact solution of 1D Burges Equation
  #1
Tian Baolin
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the Eq. u,t+u*u,x=0 u(x,0)=alpha+Pi*sin(Pi*x),-1<x<1

the analytic solution?

thanks!
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Old   May 12, 2003, 04:33
Default Re: to find the exact solution of 1D Burges Equati
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Tom
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If you mean the inviscid burgers equation (u_t + uu_x =0) then the solution is, parametrically,

u = U(s) = alpha + pi.sin(pi.s),

x = s + t.U(s)
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Old   May 12, 2003, 08:13
Default Re: to find the exact solution of 1D Burges Equati
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Tian Baolin
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Dear Tom, Thanks a lot for your solution.Yeah,I just need the solution of inviscid burgers equation.I am sorry that I had given a poor expression of my issue. Your reply is of much help for me,but could you give me a detailed explaination for me. I can't understand meanings of 's'and 'U(s)'. Thanks Again!

Yours sincerely Tian Baolin
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Old   May 13, 2003, 04:34
Default Re: to find the exact solution of 1D Burges Equati
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Tom
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s is simply a parameter if you fix t and vary s you get the values of u and corresponding values x. Another way of looking at it is to think os s as a Langrangian marker for a fluid particle. If you fix s and vary time the value of u does not change and so is equal to it's initial value U(s) while it's position (x=s at t=0) has changed due to convection.

Hope this helps - you may want to look at the book

"Linear and Nonlinear Waves" by G.B. Whitham

which discusses the Burger equation in detail,

Tom.
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