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
In the viewpoint of physics,for the Korteweg-de Vries(KdV)equation,we care the evolution effects of soliton with respect to space in perturbation theory,so the new boundary condition u→0 as t→∞is under our consider...In the viewpoint of physics,for the Korteweg-de Vries(KdV)equation,we care the evolution effects of soliton with respect to space in perturbation theory,so the new boundary condition u→0 as t→∞is under our consideration.We derive Zakharov-Shabat Equation of inverse scattering for the KdV equation under new condition starting from the second Lax equation.Finally the space dependences of scattering data are determined corresponding to time dependences of scattering data in traditional case,which are bases for developing perturbation theory under new condition.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 Foundation of China under Grant No.19775037.
文摘In the viewpoint of physics,for the Korteweg-de Vries(KdV)equation,we care the evolution effects of soliton with respect to space in perturbation theory,so the new boundary condition u→0 as t→∞is under our consideration.We derive Zakharov-Shabat Equation of inverse scattering for the KdV equation under new condition starting from the second Lax equation.Finally the space dependences of scattering data are determined corresponding to time dependences of scattering data in traditional case,which are bases for developing perturbation theory under new condition.
