    [ d_tt - d_xx ] u( t,x ) = - d_u P( u )
Solution of wave equation [ d_tt - d_xx ] u( t,x ) = - d_u P( u )

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(Non-linearity)

  
Initial interval's coordinate

***  "a" = 
***Parameter of potencial "a" =

   U( x - v * t ) 
Let's see the solution U( x - v * t ) 

***  
***There may be soliton with

   -P(U)
Potencial energy -P(U)

 -   U'=SQRT( + 2 * P(U) )
Phase plane for equation U'=SQRT( + 2 * P(U) )

   U(x):  U'' = + d [ P(U) ] / dU
Solution of ODE  U(x):  U'' = + d_U [ P(U) ] / dU


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*** 
***The adiabatic additive

***  - kAd * Cos ( wAd * x )
***Right part - kAd * Cos ( wAd * x )

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Init.interv

  
 is broken on

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parts. Means, at dx =

   t=
poss. to reach up to t =

 
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Dependence of the solution from "x" at given "t"

    "x"   "t" ( )
Dependence of density of energy from "x" at given "t" (logarithmic scale)


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