Periodic solutions and solitons to two complex short pulse (CSP) equations in optical fiber

Abstract

Two complex short pulse equations in optical fiber, namely, the focusing complex short pulse (FCSP) equation and the defocusing complex short pulse (DFCSP) equation, are investigated. By F-expansion method, a series of periodic traveling wave solutions are obtained, which involve Jacobian elliptic functions. When the modulus m→1, the solutions degenerate to the soliton solutions, respectively. Partial Jacobian elliptic solutions and soliton solutions are visualized to illustrate the propagation properties of the solutions.