4. If V(u) involved in the Klein-Gordon equation (11.5.1) is given (Whitham, 1974) by -Uxx +v'(u)...

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4. If V(u) involved in the Klein-Gordon equation (11.5.1) is given (Whitham, 1974) by -Uxx +v'(u) zo 1 V(u) =;. u'+bu* +.., 11.13 Exercises 497 derive the result = a cos 0+-a'b cos 30+ ..., 8. as a→0, where the nonlinear dispersion relation is given by o? = 1+k +3a*b+o(a), as a→0, and the nonlinear amplitude is 1 9. A =-a' +-a'b+o(a*) as a →0. 4. If V(u) involved in the Klein-Gordon equation (11.5.1) is given (Whitham, 1974) by -Uxx +v'(u) zo 1 V(u) =;. u'+bu* +.., 11.13 Exercises 497 derive the result = a cos 0+-a'b cos 30+ ..., 8. as a→0, where the nonlinear dispersion relation is given by o? = 1+k +3a*b+o(a), as a→0, and the nonlinear amplitude is 1 9. A =-a' +-a'b+o(a*) as a →0.

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