With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we invest...With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.展开更多
Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented i...Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.展开更多
On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensiona...On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.展开更多
基金the Natural Science Foundation of Zhejiang Province under Grant No.Y606128the Natural Science Foundation of Zhejiang Lishui University under Grant No.KZ08001the Scientific Research Fund of the Education Department of Zhejiang Province under Grant No.20070568
文摘With the help of the conditional similarity reduction method, some new exact solutions of the （2＋1）- dimensional modified dispersive water-wave system （MDWW） are obtained. Based on the derived solution, we investigate the evolution of solitons in the background waves.
基金The project supported by the Alexander von Humboldt Foundationthe Youth Foundation of Shanghai Jiao Tong UniversityNational Natural Science Foundation of China under Grant No.10475055
文摘Applying the classical Lie symmetry approach to the barotropic and quasi-geostrophic potential vorticity equation without forcing and dissipation on a β-plane channel, we find a new symmetry, which is not presented in a previous work [F. Huang, Commun. Theor. Phys. （Beijing, China） 42 （2004） 903]. A general finite transformation group is obtained based on the full Lie point symmetry, Furthermore, two new types of similarity reduction solutions are obtained.
基金supported by National Natural Science Foundation of China under Grant Nos.10735030 and 90718141Shanghai Leading Academic Discipline Project under Grant No.B412+3 种基金Natural Science Foundations of Zhejiang Province of China under Grant No.Y604056Doctoral Foundation of Ningbo City under Grant No.2005A61030Program for Changjiang Scholars and Innovative Research Team in University under Grant No.IRT0734K.C.Wang Magna Fund in Ningbo University
文摘On bases of the direct method developed by Clarkson and Kruskal [J.Math.Phys.27 (1989) 2201],the(2+1)-dimensional nonisospectral Kadomtsev-Petviashvili (KP) equation has been reduced to three types of (1+1)-dimensional partial differential equations.We focus on solving the third type of reduction and dividing them into threesubcases,from which we obtain rich solutions including some arbitrary functions.
