A novel hierarchy of integrable nonlinear evolution equations related to the combined Ablowitz–Kaup–Newell–Segur（AKNS） and Wadati–Konno–Ichikawa（WKI） spectral problems is proposed,from which the Lax pair for ...A novel hierarchy of integrable nonlinear evolution equations related to the combined Ablowitz–Kaup–Newell–Segur（AKNS） and Wadati–Konno–Ichikawa（WKI） spectral problems is proposed,from which the Lax pair for a corresponding negative flow and its infinite many conservation laws are obtained.Furthermore,a reduction of this hierarchy is discussed,by which a generalized sinh-Gordon equation is derived on the basis of its negative flow.展开更多
We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann bo...We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.展开更多
基金Project supported by the National Natural Science Foundation of China(Grant Nos.11501520 and 11331008)the Outstanding Young Talent Research Fund of Zhengzhou University(Grant No.1521315001)
文摘A novel hierarchy of integrable nonlinear evolution equations related to the combined Ablowitz–Kaup–Newell–Segur（AKNS） and Wadati–Konno–Ichikawa（WKI） spectral problems is proposed,from which the Lax pair for a corresponding negative flow and its infinite many conservation laws are obtained.Furthermore,a reduction of this hierarchy is discussed,by which a generalized sinh-Gordon equation is derived on the basis of its negative flow.
文摘We consider a Hilbert boundary value problem with an unknown parametric function on arbitrary infinite straight line passing through the origin. We propose to transform the Hilbert boundary value problem to Riemann boundary value problem, and address it by defining symmetric extension for holomorphic functions about an arbitrary straight line passing through the origin. Finally, we develop the general solution and the solvable conditions for the Hilbert boundary value problem.
