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 Post subject: integral of differential equationPosted: Mon, 9 Apr 2012 12:23:34 UTC
 Senior Member

Joined: Thu, 22 Jun 2006 01:08:00 UTC
Posts: 136
hi, i am confused with this integral, the problem reads:

given the D.E. (KdV equation), denote the soliton solution by where represents the shape of the soliton and the speed. Write the equation for by substituting in the soliton equation, integrate once and show that the constant of integration vanishes using the fact that the has to decay at infinity.

what i have done
taking

And then I don't know what to do, any idea?

thanks!

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 Post subject: Re: integral of differential equationPosted: Mon, 9 Apr 2012 12:28:10 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7623
Location: NCTS/TPE, Taiwan
ender wrote:
hi, i am confused with this integral, the problem reads:

given the D.E. (KdV equation), denote the soliton solution by where represents the shape of the soliton and the speed. Write the equation for by substituting in the soliton equation, integrate once and show that the constant of integration vanishes using the fact that the has to decay at infinity.

what i have done
taking

And then I don't know what to do, any idea?

thanks!

What are the doing here? Once you correct that, follow the instruction
Quote:
integrate once and ...

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 Post subject: Re: integral of differential equationPosted: Mon, 9 Apr 2012 12:46:43 UTC
 Senior Member

Joined: Thu, 22 Jun 2006 01:08:00 UTC
Posts: 136
well yes here dx=1 and dt=1 but still i get then the equation

integrating we have

right?
but i think the solution i should get is

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 Post subject: Re: integral of differential equationPosted: Mon, 9 Apr 2012 12:49:29 UTC
 Moderator

Joined: Mon, 29 Dec 2008 17:49:32 UTC
Posts: 7623
Location: NCTS/TPE, Taiwan
ender wrote:
well yes here dx=1 and dt=1 but still i get then the equation

integrating we have

right?
but i think the solution i should get is

Huh? What is this mysterious you have in the denominator here? And you haven't shown why the RHS is zero...

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 Post subject: Re: integral of differential equationPosted: Mon, 9 Apr 2012 13:08:14 UTC
 Senior Member

Joined: Thu, 22 Jun 2006 01:08:00 UTC
Posts: 136
sorry the denominator is not an S is a 2, (typo). The RHS is 0 because it the profile decays at x=infinity and this also holds fot t=0, it follows from this.

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