9. (a) Use the Bcklund transformation (11.9.2ab) to show that four solutions u, (r=1,2,3,4) satisfy the relation tan - (- (- - -)} = (2+2) - { (-4,-2) - { tan- a-a where a and 92 are nonzero constants. (b) Apply the relation in Exercise 9(a) to obtain a soliton solution of the sine-Gordon equation by setting u, 0, and u, different soliton solutions. 10. Examine the asymptotic nature of the two-soliton solution (11.10.19), as . 11. Derive the solitary wave solution of the sinh-Gordon equation = sinh. (1101) of the - (u - v), 2 1 1 1 = a sin u + b), u+ 0), = = sin - (u - ), (11.9.2ab) 2 2 -2