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The Nonlinear Klein-Gordon Equation
[chapter]
2014
Springer Monographs in Mathematics
7. ∂ 2 w ∂t 2 = ∂ 2 w ∂x 2 + f (w). Nonlinear Klein-Gordon equation. 1 • . Suppose w = w(x, t) is a solution of the nonlinear Klein-Gordon equation. Then the functions where C 1 , C 2 , and β are arbitrary constants, are also solutions of the equation (the plus or minus signs in w 1 are chosen arbitrarily). 2 • . Traveling-wave solution in implicit form: where C 1 , C 2 , k, and λ are arbitrary constants. 3 • . Functional separable solution: where C 1 and C 2 are arbitrary constants, and the
doi:10.1007/978-3-319-06914-2_4
fatcat:dxbsn2abivclpg7knovqtdnvqq