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  3. consider the sine-gordon equation (sge) ?xt =sin?,

Consider the sine-Gordon equation (SGE) ?xt =sin?, (1) which governs a function ?(x,t). For any given ?...

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Advance Math

Consider the sine-Gordon equation (SGE)
?xt =sin?, (1)

which governs a function ?(x,t). For any given ? denote thefollowing B ?acklund trans- formation by BT?:

1
? ??x=2?sin 2(? +?) , (2a)

2 1
? +?t=?sin 2(? ??) , (2b)

  1. (a) Given a solution ?(x, t) of the SGE, show that ?(x, t) alsosatisfies the SGE. Hint: Try calculating the t derivative ofEquation (2a) and the x-derivative of Equation (2b) and then takinga sum or difference.

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SolGiven the sineGordon equation SGE1Also for any denotethefollowing    See Answer
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