Superposed periodic kink and pulse solutions of coupled nonlinear equations

We present novel previously unexplored periodic solutions, ex-pressed in terms of Jacobi elliptic functions, for both a coupled phi 4 model and a coupled nonlinear Schrodinger equation (NLS) model. Remarkably, these solutions can be elegantly reformu-lated 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.(c) 2023 Elsevier Inc. All rights reserved.