A new integrable system of symmetrically coupled derivative nonlinear Schrödinger equations via the singularity analysis

A new integrable system of two symmetrically coupled derivative nonlinear Schrödinger equations is detected by means of the singularity analysis. A nonlinear transformation is proposed which uncouples the equations of the new system. In this paper, we study the integrability of the following system of two symmetrically coupled derivative nonlinear Schrödinger equations: qt = iqxx + aqq̄qx + bq q̄x + crr̄qx + dqr̄rx + eqrr̄x + ifq q̄ + igqrr̄, rt = irxx + arr̄rx + br r̄x + cqq̄rx + drq̄qx + erqq̄x + ifr r̄ + igrqq̄, (1) where a, b, c, d, e, f, g are real parameters, and the bar denotes the complex conjugation. By means of the singularity analysis, we detect one new integrable case of the system (1), characterized by the conditions a = c = e 6= 0, b = d = g = 0. (2) Then we propose a nonlinear transformation, which uncouples the equations (1) in the case (2).