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The integrable time-dependent sine-Gordon equation with multiple optical kink solutions

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Abstract In this work, we study the sine-Gordon equation with time-dependent coefficient. We show that this time-dependent equation passes the Painleve test for any analytic time-dependent coefficient. This confirms its… Click to show full abstract

Abstract In this work, we study the sine-Gordon equation with time-dependent coefficient. We show that this time-dependent equation passes the Painleve test for any analytic time-dependent coefficient. This confirms its integrability in a like manner to the standard sine-Gordon equation with constant coefficients. Multiple real and multiple complex optical kink solutions will be reported.

Keywords: sine gordon; gordon equation; optical kink; equation; time dependent

Journal Title: Optik
Year Published: 2019

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