The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the ...The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.展开更多
A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform.The two-sheeted Riemann surface associated with the boundary problem is transformed into the...A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform.The two-sheeted Riemann surface associated with the boundary problem is transformed into the Riemann sphere by introducing a suitable variable transformation.The associated spectral properties of the lattice in single-valued variable was discussed.The constraint condition about the nonzero boundary condition and the scattering data is found.展开更多
基金supported by the National Natural Science Foundation of China under Grant No.11975306the Natural Science Foundation of Jiangsu Province under Grant No.BK20181351+1 种基金the Six Talent Peaks Project in Jiangsu Province under Grant No.JY-059the Fundamental Research Fund for the Central Universities under the Grant Nos.2019ZDPY07 and 2019QNA35。
文摘The present work studies the inverse scattering transforms(IST)of the inhomogeneous fifth-order nonlinear Schrodinger(NLS)equation with zero boundary conditions(ZBCs)and nonzero boundary conditions(NZBCs).Firstly,the bound-state solitons of the inhomogeneous fifth-order NLS equation with ZBCs are derived by the residue theorem and the Laurent's series for the first time.Then,by combining with the robust IST,the Riemann-Hilbert(RH)problem of the inhomogeneous fifth-order NLS equation with NZBCs is revealed.Furthermore,based on the resulting RH problem,some new rogue wave solutions of the inhomogeneous fifth-order NLS equation are found by the Darboux transformation.Finally,some corresponding graphs are given by selecting appropriate parameters to further analyze the unreported dynamic characteristics of the corresponding solutions.
基金This work was supported by the National Natural Science Foundation of China(Grant No.11471295)The third author’s work was partially supported by the President’s Endowed Professorship program of the University of Texas system.
文摘A generalized Volterra lattice with a nonzero boundary condition is considered by virtue of the inverse scattering transform.The two-sheeted Riemann surface associated with the boundary problem is transformed into the Riemann sphere by introducing a suitable variable transformation.The associated spectral properties of the lattice in single-valued variable was discussed.The constraint condition about the nonzero boundary condition and the scattering data is found.
