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Solving the Klein-Gordon equation by means of the homotopy analysis method. (English) Zbl 1078.35105
Summary: An analytic technique, namely the homotopy analysis method, is applied to solve the nonlinear travelling waves governed by the Klein-Gordon equation. The phase speed and the solution, which are dependent on the amplitude $a$, are given and valid in the whole region $0\leqslant a < +\infty$.

35Q53KdV-like (Korteweg-de Vries) equations
37K40Soliton theory, asymptotic behavior of solutions
81Q05Closed and approximate solutions to quantum-mechanical equations
Full Text: DOI
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