By using holomorphic Riemannian geometry in C^3, the coupled Landau-Lifshitz(CLL) equation is proved to be exactly the equation of Schr¨odinger flows from R^1 to the complex 2-sphere CS^2(1) → C^3.Furthermore, r...By using holomorphic Riemannian geometry in C^3, the coupled Landau-Lifshitz(CLL) equation is proved to be exactly the equation of Schr¨odinger flows from R^1 to the complex 2-sphere CS^2(1) → C^3.Furthermore, regarded as a model of moving complex curves in C^3, the CLL equation is shown to preserve the PT symmetry if the initial data is of the P symmetry. As a consequence, the nonlocal nonlinear Schrodinger(NNLS)equation proposed recently by Ablowitz and Musslimani is proved to be gauge equivalent to the CLL equation with initial data being restricted by the P symmetry. This gives an accurate characterization of the gaugeequivalent magnetic structure of the NNLS equation described roughly by Gadzhimuradov and Agalarov(2016).展开更多
The new coupled MKdV hierarchy is obtained. By using gauge transformation, the constrained flow, the integrable system and Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarc...The new coupled MKdV hierarchy is obtained. By using gauge transformation, the constrained flow, the integrable system and Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarchy and then using the Lax representation, the r_matrix for the constrained flow of the coupled MKdV hierarchy was constructed. The second set of conserved integrals of this constrained flow and their involutivity were also given.展开更多
基金supported by National Natural Science Foundation of China(Grant No.11271073)。
文摘By using holomorphic Riemannian geometry in C^3, the coupled Landau-Lifshitz(CLL) equation is proved to be exactly the equation of Schr¨odinger flows from R^1 to the complex 2-sphere CS^2(1) → C^3.Furthermore, regarded as a model of moving complex curves in C^3, the CLL equation is shown to preserve the PT symmetry if the initial data is of the P symmetry. As a consequence, the nonlocal nonlinear Schrodinger(NNLS)equation proposed recently by Ablowitz and Musslimani is proved to be gauge equivalent to the CLL equation with initial data being restricted by the P symmetry. This gives an accurate characterization of the gaugeequivalent magnetic structure of the NNLS equation described roughly by Gadzhimuradov and Agalarov(2016).
文摘The new coupled MKdV hierarchy is obtained. By using gauge transformation, the constrained flow, the integrable system and Lax representation for the coupled MKdV hierarchy were first constructed from the AKNS hierarchy and then using the Lax representation, the r_matrix for the constrained flow of the coupled MKdV hierarchy was constructed. The second set of conserved integrals of this constrained flow and their involutivity were also given.
