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A method for generating exact solutions of the nonlinear Klein-Gordon equation. (English) Zbl 0991.35529

Summary: We propose a simple method for generating the exact solutions of the nonlinear Klein-Gordon equation. The solutions obtained depend on two arbitrary functions and are in the form of running waves. An application of one of the solutions for the \((2+1)\)-dimensional sine-Gordon equation is proposed. It concerns the selective properties of a two-dimensional semi-infinite Josephson junction with regard to an external electromagnetic field in the form of running waves with a phase velocity equal to the Swihart velocity. A method for measuring the Swihart velocity is presented.

MSC:

35Q40 PDEs in connection with quantum mechanics
35L70 Second-order nonlinear hyperbolic equations
81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics
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