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arXiv · 2301.02028

Superposed periodic kink and pulse solutions of coupled nonlinear equations

Avinash Khare·Saikat Banerjee·Avadh Saxena
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Abstract

We present novel previously unexplored periodic solutions, expressed in terms of Jacobi elliptic functions, for both a coupled $ϕ^4$ model and a coupled nonlinear Schrödinger equation (NLS) model. Remarkably, these solutions can be elegantly reformulated as a linear combination of periodic kinks and antikinks, or as a combination of two periodic kinks or two periodic pulse solutions. However, we also find that for $m=0$ and a specific value of the periodicity (or at a nonzero value of the elliptic modulus $m$) this superposition does not hold. These results demonstrate that the notion of superposed solutions extends to the coupled nonlinear equations as well.

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Avinash Khare, Saikat Banerjee, Avadh Saxena. 2023-08-14. Superposed periodic kink and pulse solutions of coupled nonlinear equations. https://doi.org/10.1016/j.aop.2023.169433

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