14. Using the Lagrangian density 1 where V'(u)= sin u, derive the sine-Gordon equation %3D -u...

 

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14. Using the Lagrangian density 1 where V'(u)= sin u, derive the sine-Gordon equation %3D "-u = sin u. 15. Show that the bilinear form of the sine-Gordon equation in Exercise 14 is the pair of equations %3D (D - D -1)(*-w)=0 and (D - D})(+•0- w• w) = 0, (). where u = 4 tan 14. Using the Lagrangian density 1 where V'(u)= sin u, derive the sine-Gordon equation %3D "-u = sin u. 15. Show that the bilinear form of the sine-Gordon equation in Exercise 14 is the pair of equations %3D (D - D -1)(*-w)=0 and (D - D})(+•0- w• w) = 0, (). where u = 4 tan