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arXiv · 2610.36891

Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence

Thokala Soloman Raju·T. Shreecharan·Avinash Khare·Avadh Saxena
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Abstract

By using suitable ansatz which reduces the problem of obtaining exact solutions of the sine-Gordon equation with nontrivial time dependence to obtaining exact solutions of two first order symmetric $ϕ^4$-like coupled equations in $x$ and $t$, we obtain a large number of hyperbolic and periodic solutions of the sine-Gordon equation. In particular, we not only obtain the well-known two-soliton, soliton-antisoliton and the breather solutions but also obtain periodic two-soliton, periodic soliton-antisoliton as well as periodic breather solutions. Besides, we also obtain superposed real and complex (parity-time reversal or) $\mathcal{PT}$-invariant solutions related to the two-soliton, soliton-antisoliton and the breather solutions of the sine-Gordon equation.

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Thokala Soloman Raju, T. Shreecharan, Avinash Khare, Avadh Saxena. 2026-10-27. Large number of hyperbolic and periodic solutions of sine-Gordon equation with nontrivial time dependence. https://arxiv.org/abs/2610.36891

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