The bilinear form of the （2＋1）-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a （2＋1）-dimensional non-isospectral Schrodinger...The bilinear form of the （2＋1）-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a （2＋1）-dimensional non-isospectral Schrodinger equation and its N-soliton solutions are constructed.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
In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the...In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 〈 θ 〈 -θ=arctan 1/（√2＋√5）, where θ is the half angle of the wedge. Furthermore, they get the uniform C^1,1 estimates of the solution to the expansion problem.展开更多
基金The project supported by National Natural Science Foundation of China under Grant No. 10371070 and the Special Funds for Major Specialities of Shanghai Education Committee
文摘Bilinear form of the nonisospectral AKNS equation is given. The N-soliton solutions are obtained through Hirota＇s method.
基金supported by China Postdoctoral Science Foundation and National Natural Science Foundation of China under Grant No.10771207
文摘The bilinear form of the （2＋1）-dimensional non-isospectral AKNS system is derived. Its N-soliton solutions are obtained by using the Hirota method. As a reduction, a （2＋1）-dimensional non-isospectral Schrodinger equation and its N-soliton solutions are constructed.
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.
基金supported by the National Natural Science Foundation of China(No.11371240)Shanghai Municipal Education Commission of Scientific Research Innovation Project(No.11ZZ84)+1 种基金the Fundamental Research Funds for the Central Universities(No.15CX02074A)the grant of “the First-Class Discipline of Universities in Shanghai”
文摘In this paper, the authors consider the expansion problem of a wedge of gas into vacuum for the two-dimensional Euler equations in isothermal flow. By the bootstrapping argument, they prove the global existence of the smooth solution through the direct method in the case 0 〈 θ 〈 -θ=arctan 1/（√2＋√5）, where θ is the half angle of the wedge. Furthermore, they get the uniform C^1,1 estimates of the solution to the expansion problem.
