Coupled Nonlinear Schrödinger Equations and the Miura Transformation
LOU Yan1, ZHU Jun-Yi2**
1College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450052 2Department of Mathematics, Zhengzhou University, Zhengzhou 450052
Coupled Nonlinear Schrödinger Equations and the Miura Transformation
LOU Yan1, ZHU Jun-Yi2**
1College of Mathematics and Information Science, North China University of Water Resources and Electric Power, Zhengzhou 450052 2Department of Mathematics, Zhengzhou University, Zhengzhou 450052
摘要A wide class of coupled nonlinear Schrödinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with σ1 is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.
Abstract：A wide class of coupled nonlinear Schrödinger (NLS) equations are derived by virtue of the dressing method, and the associated parametric solutions are discussed. As an illustration, the explicit solution of the coupled NLS-type equation associated with σ1 is given. The Miura transformation for a AKNS-type hierarchy is established, from which a modified coupled NLS-type equation is shown to be equivalent to the Heisenberg spin equation.
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2011, Vol. 28 
