A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing....A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.展开更多
For ion-acoustic waves in a plasma with non-isothermal electrons, the MKP equation is its governing equation. The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is i...For ion-acoustic waves in a plasma with non-isothermal electrons, the MKP equation is its governing equation. The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is investigated up to the third order. It indicates that the one-soliton solution of MKP equation is unstable if v = -1 wheras it is stable if v = 1 until the third order approximation has been considered.展开更多
An extended form of the modified Kadomtsev-Petviashvili （mKP） equation is investigated. The simplified form of the Hirota bilinear method established by Hereman and Nuseir is employed. Multi-front wave solutions are...An extended form of the modified Kadomtsev-Petviashvili （mKP） equation is investigated. The simplified form of the Hirota bilinear method established by Hereman and Nuseir is employed. Multi-front wave solutions are formally derived to the extended mKP equation and the mKP equation. The results show that the extension terms do not kill the integrability of the mKP equation.展开更多
基金supported by National Natural Science Foundation of China under Grant No. 10575087the Natural Science Foundation of Zhejiang Province under Grant No. 102053
文摘A new nonlinear partial differential equation （PDE） in 2＋1 dimensions is obtained from the mKP equation by means of an asymptotically exact reduction method based on Fourier expansion and spatio-temporal resealing. In order to demonstrate integrability property of the new equation, the corresponding Lax pair is obtained by applying the reduction technique to the Lax pair of the mKP equation.
文摘For ion-acoustic waves in a plasma with non-isothermal electrons, the MKP equation is its governing equation. The instability of a soliton solution of MKP equation to two-dimensional long-wavelength perturbations is investigated up to the third order. It indicates that the one-soliton solution of MKP equation is unstable if v = -1 wheras it is stable if v = 1 until the third order approximation has been considered.
文摘An extended form of the modified Kadomtsev-Petviashvili （mKP） equation is investigated. The simplified form of the Hirota bilinear method established by Hereman and Nuseir is employed. Multi-front wave solutions are formally derived to the extended mKP equation and the mKP equation. The results show that the extension terms do not kill the integrability of the mKP equation.
