Exact solutions and asymptotic solutions of one-dimensional domain walls in nonlinearly coupled system

We use homotopy renormalization method to investigate one-dimensional radial domain wall modes in the system of two nonlinear Schrodinger or Gross–Pitaevskii equations, which are coupled by linear mixing and by nonlinear XPM (cross-phase-modulation). The asymptotic solutions satisfying the boundary conditions are given by taking the inhomogeneous variable coefficient homotopy equations. To our knowledge, this is the first time that the inhomogeneous variable coefficient homotopy equations are taken. Moreover, the comparisons with numerical results show that our explicit function solutions have good performances in both local and large scale. In particular, in some conditions with special parameters, the asymptotic solutions are actually the exact solutions.