Periodic solutions for systems of coupled nonlinear Schrödinger equations with three and four components.

Periodic solutions for systems of coupled nonlinear Schrödinger equations (CNLS) are established by the Hirota bilinear method and elliptic functions. The interesting feature is the choice of theta functions in the formulation. The sum of moduli of the components or the total intensity of the beam in physical terms, will now be a rational function, instead of a polynomial, of elliptic functions. Each component of the CNLS may have multiple peaks within one period.

Periodic solutions for systems of coupled nonlinear Schrödinger equations with five and six components.

Systems of coupled nonlinear Schrödinger (CNLS) equations arise in several branches of physics, e.g., optics and plasma physics. Systems with two or three components have been studied intensively. Recently periodic solutions for CNLS systems with four components are derived. The present work extends the search of periodic solutions for CNLS systems to those with five and six components. The Hirota bilinear method, theta and elliptic functions are employed in the process. The long wave limit is studied, and known results of solitary waves are recovered. The validity of these periodic solutions is verified independently by direct differentiation with computer algebra software.