Dynamics of solitons to the coupled sine-Gordon equation in nonlinear optics

Abstract

This paper employs the principle of undetermined coefficients to establish the hyperbolic and trigonometric function solutions of the coupled sine-Gordon equation (CSGE) which describes the propagation of an optical pulse in fiber waveguide. Lie point symmetry of the CSGE is derived. Previously, it was noticed that the concept of nonlinear self-adjointness (NSA) was not applied on the equation under consideration. Here, we apply the concept of NSA to find an explicit form of the differential substitution. By means of the obtained substitution, we establish a new variant of conserved vectors by a new conservation theorem.