Superposed periodic kink and pulse solutions of coupled nonlinear equations

Abstract

We present novel previously unexplored periodic solutions, expressed in terms of Jacobi elliptic functions, for both a coupled ${\varphi }^4$ 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.

arXiv commentFinal published version

References in corpus (8)

• Full Phase Diagram of the Massive Gross-Neveu Model
• Integrable nonlocal Hirota equations
• Long-time asymptotics for the Nonlocal mKdV equation
• Linear Superposition for a Large Number of Nonlinear Equations
• Superposition of Elliptic Functions as Solutions For a Large Number of Nonlinear Equations
• Novel PT-invariant Solutions For a Large Number of Real Nonlinear Equations
• Novel Superposed Kinklike and Pulselike Solutions for Several Nonlocal Nonlinear Equations
• Superposed Hyperbolic Kink and Pulse Solutions of Coupled ${\varphi }^4$, NLS and MKdV Equations