Abstract
We present novel previously unexplored periodic solutions, expressed in terms of Jacobi elliptic functions, for both a coupled ϕ4 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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