Inviscid Burgers equation — multivalued wave

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I'm quite new to Wolfram Mathematica. I need to create an animation of a Burgers Hopf equation's solution which becomes multivalued (somewhat of a breaking wave). Is it possible to do so in Mathematica?



All I seem to obtain is a very sharp series of oscillations which I assume are a numerical correction by the software.



Any help will be appreciated.



NDSolve[
 D[u[x, t], t] + 1/2 D[u[x, t]^2, x] == 0, 
 u[x, 0] == Sech[x]^2, u[-5, t] == u[5, t], 
 u[x, t], x, -5, 5, t, 0, 5]`



differential-equations nonlinear




share|improve this question

















  • 1




    There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
    – Kuba♦
    Aug 6 at 12:41










  • i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
    – ddot
    Aug 6 at 12:54










  • I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
    – Kuba♦
    Aug 6 at 12:58






  • 1




    What do you mean by c-shaped wave? Can you be more specific?
    – xzczd
    Aug 6 at 13:04










  • i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
    – ddot
    Aug 6 at 13:12














up vote
4
down vote

favorite












I'm quite new to Wolfram Mathematica. I need to create an animation of a Burgers Hopf equation's solution which becomes multivalued (somewhat of a breaking wave). Is it possible to do so in Mathematica?



All I seem to obtain is a very sharp series of oscillations which I assume are a numerical correction by the software.



Any help will be appreciated.



NDSolve[
 D[u[x, t], t] + 1/2 D[u[x, t]^2, x] == 0, 
 u[x, 0] == Sech[x]^2, u[-5, t] == u[5, t], 
 u[x, t], x, -5, 5, t, 0, 5]`



differential-equations nonlinear




share|improve this question

















  • 1




    There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
    – Kuba♦
    Aug 6 at 12:41










  • i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
    – ddot
    Aug 6 at 12:54










  • I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
    – Kuba♦
    Aug 6 at 12:58






  • 1




    What do you mean by c-shaped wave? Can you be more specific?
    – xzczd
    Aug 6 at 13:04










  • i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
    – ddot
    Aug 6 at 13:12












up vote
4
down vote

favorite









up vote
4
down vote

favorite











I'm quite new to Wolfram Mathematica. I need to create an animation of a Burgers Hopf equation's solution which becomes multivalued (somewhat of a breaking wave). Is it possible to do so in Mathematica?



All I seem to obtain is a very sharp series of oscillations which I assume are a numerical correction by the software.



Any help will be appreciated.



NDSolve[
 D[u[x, t], t] + 1/2 D[u[x, t]^2, x] == 0, 
 u[x, 0] == Sech[x]^2, u[-5, t] == u[5, t], 
 u[x, t], x, -5, 5, t, 0, 5]`



differential-equations nonlinear




share|improve this question













I'm quite new to Wolfram Mathematica. I need to create an animation of a Burgers Hopf equation's solution which becomes multivalued (somewhat of a breaking wave). Is it possible to do so in Mathematica?



All I seem to obtain is a very sharp series of oscillations which I assume are a numerical correction by the software.



Any help will be appreciated.



NDSolve[
 D[u[x, t], t] + 1/2 D[u[x, t]^2, x] == 0, 
 u[x, 0] == Sech[x]^2, u[-5, t] == u[5, t], 
 u[x, t], x, -5, 5, t, 0, 5]`




differential-equations nonlinear





share|improve this question












share|improve this question




share|improve this question








edited Aug 6 at 13:52
























asked Aug 6 at 12:35









ddot

212




212







  • 1




    There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
    – Kuba♦
    Aug 6 at 12:41










  • i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
    – ddot
    Aug 6 at 12:54










  • I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
    – Kuba♦
    Aug 6 at 12:58






  • 1




    What do you mean by c-shaped wave? Can you be more specific?
    – xzczd
    Aug 6 at 13:04










  • i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
    – ddot
    Aug 6 at 13:12












  • 1




    There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
    – Kuba♦
    Aug 6 at 12:41










  • i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
    – ddot
    Aug 6 at 12:54










  • I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
    – Kuba♦
    Aug 6 at 12:58






  • 1




    What do you mean by c-shaped wave? Can you be more specific?
    – xzczd
    Aug 6 at 13:04










  • i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
    – ddot
    Aug 6 at 13:12







1




1




There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
– Kuba♦
Aug 6 at 12:41




There are examples of plots, even dynamic with Manipulate, on NDSolve documentation page. Have you seen them?
– Kuba♦
Aug 6 at 12:41












i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
– ddot
Aug 6 at 12:54




i have seen them but nothing seems to create the animation i need, which is a c- shaped wave
– ddot
Aug 6 at 12:54












I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
– Kuba♦
Aug 6 at 12:58




I don't think you can get c-shaped wave, nor wiki page shows them. But you create a steep one with your solution.
– Kuba♦
Aug 6 at 12:58




1




1




What do you mean by c-shaped wave? Can you be more specific?
– xzczd
Aug 6 at 13:04




What do you mean by c-shaped wave? Can you be more specific?
– xzczd
Aug 6 at 13:04












i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
– ddot
Aug 6 at 13:12




i mean an animation of a gaussian like wave in which the upper portion goes faster tham the lower one, so it creates sort of a breaking wave, but kuba confirmed my suspects, it's probably not possible to obtain in Mathematica
– ddot
Aug 6 at 13:12










1 Answer
1






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votes

















up vote
5
down vote













I don't think NDSolve is the right tool for the task, because it can only solve for single-valued functions. (Well, is there any mathematical software that can deal with multi-valued functions natively? ) Fortunately, your goal is just creating an animation for the multi-valued solution, then we can simply refer to the analytic solution of this problem:



Animate[ParametricPlot[t f[ξ] + ξ, f[ξ], ξ, -5, 5, 
 AspectRatio -> 1/GoldenRatio], t, 0, 5]


enter image description here






share|improve this answer





















  • thank you very much :)
    – ddot
    Aug 6 at 15:40










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1 Answer
1






active

oldest

votes








1 Answer
1






active

oldest

votes









active

oldest

votes






active

oldest

votes








up vote
5
down vote













I don't think NDSolve is the right tool for the task, because it can only solve for single-valued functions. (Well, is there any mathematical software that can deal with multi-valued functions natively? ) Fortunately, your goal is just creating an animation for the multi-valued solution, then we can simply refer to the analytic solution of this problem:



Animate[ParametricPlot[t f[ξ] + ξ, f[ξ], ξ, -5, 5, 
 AspectRatio -> 1/GoldenRatio], t, 0, 5]


enter image description here






share|improve this answer





















  • thank you very much :)
    – ddot
    Aug 6 at 15:40














up vote
5
down vote













I don't think NDSolve is the right tool for the task, because it can only solve for single-valued functions. (Well, is there any mathematical software that can deal with multi-valued functions natively? ) Fortunately, your goal is just creating an animation for the multi-valued solution, then we can simply refer to the analytic solution of this problem:



Animate[ParametricPlot[t f[ξ] + ξ, f[ξ], ξ, -5, 5, 
 AspectRatio -> 1/GoldenRatio], t, 0, 5]


enter image description here






share|improve this answer





















  • thank you very much :)
    – ddot
    Aug 6 at 15:40












up vote
5
down vote










up vote
5
down vote









I don't think NDSolve is the right tool for the task, because it can only solve for single-valued functions. (Well, is there any mathematical software that can deal with multi-valued functions natively? ) Fortunately, your goal is just creating an animation for the multi-valued solution, then we can simply refer to the analytic solution of this problem:



Animate[ParametricPlot[t f[ξ] + ξ, f[ξ], ξ, -5, 5, 
 AspectRatio -> 1/GoldenRatio], t, 0, 5]


enter image description here






share|improve this answer













I don't think NDSolve is the right tool for the task, because it can only solve for single-valued functions. (Well, is there any mathematical software that can deal with multi-valued functions natively? ) Fortunately, your goal is just creating an animation for the multi-valued solution, then we can simply refer to the analytic solution of this problem:



Animate[ParametricPlot[t f[ξ] + ξ, f[ξ], ξ, -5, 5, 
 AspectRatio -> 1/GoldenRatio], t, 0, 5]


enter image description here







share|improve this answer













share|improve this answer



share|improve this answer











answered Aug 6 at 14:58









xzczd

23.6k363223




23.6k363223











  • thank you very much :)
    – ddot
    Aug 6 at 15:40
















  • thank you very much :)
    – ddot
    Aug 6 at 15:40















thank you very much :)
– ddot
Aug 6 at 15:40




thank you very much :)
– ddot
Aug 6 at 15:40












 

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