Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved ...Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform.展开更多
The variable Sine-Gordon (VSG) equation is often used to model several kinds of systems with inhomogeneity and it can be realized by the management of dispersion and nonlinearity in optics and Feschbach resonance in B...The variable Sine-Gordon (VSG) equation is often used to model several kinds of systems with inhomogeneity and it can be realized by the management of dispersion and nonlinearity in optics and Feschbach resonance in Bose-Einstein condensates.We derive four new kinds of non-rational rogue wave (RW) of the VSG by using an explicit transformation and the designable integrability.These RWs have novel profiles and interesting internal structures.It is shown that the RW is induced by the inhomogeneity of the system modeled by the VSG.The theoretical prediction of the corresponding relations between the RWs and some extreme events in DNA is discussed.展开更多
文摘Hamiltonian formalism of the mKdV equation with non-vanishing boundary valueis re-examined by a revised form of the standard procedure. It is known that the previous papers did not give the final results and involved some questionable points [T.C. Au Yeung and P.C.W. Fung, J. Phys. A 21 (1988) 3575]. In this note, simple results are obtained in terms of an affine parameter and a Galileo transformation is introduced to ensure the results compatible with those derived from the inverse scattering transform.
基金Supported by the National Natural Science of China under Grant No 10971109the K.C.Wong Magna Fund in Ningbo University and Scientific Research Fund of Zhejiang Provincial Education Department under Grant No Y201017148+1 种基金the Program for NCET under Grant No NCET-08-0515Natural Science Foundation of Ningbo under Grant No 2011A610179.
文摘The variable Sine-Gordon (VSG) equation is often used to model several kinds of systems with inhomogeneity and it can be realized by the management of dispersion and nonlinearity in optics and Feschbach resonance in Bose-Einstein condensates.We derive four new kinds of non-rational rogue wave (RW) of the VSG by using an explicit transformation and the designable integrability.These RWs have novel profiles and interesting internal structures.It is shown that the RW is induced by the inhomogeneity of the system modeled by the VSG.The theoretical prediction of the corresponding relations between the RWs and some extreme events in DNA is discussed.
