Painlevé analysis and reducibility to the canonical form for the nonlinear generalized Schrödinger equation

TL;DRAbstract

We apply the Painleve test to the most general nonlinear Schrodinger-type equation: iu t + P(t)u x x -2Q(t)‖u‖2 u - (A(x, t) + iA 1 (x, t))u + (R(x, t) + iRi (x, t))u x + B(x, t) + iB 1 (x, t) = 0 in order to establishits complete integrability. The equation possesses the Painleve property when its coefficients functions satisfy suitable constraints. Assuming these constraints, the general nonlinear Schrodinger equation may be mapped to its well-known constant coefficient version by a change of independent and dependent variables.

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