In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-...In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.展开更多
A new high-dimensional two-place Alice–Bob-Kadomtsev–Petviashvili(AB-KP)equation is proposed by applying the Alice–Bob-Bob–Alice principle and shifted-parity,delayed time reversal,charge conjugation(■)principle t...A new high-dimensional two-place Alice–Bob-Kadomtsev–Petviashvili(AB-KP)equation is proposed by applying the Alice–Bob-Bob–Alice principle and shifted-parity,delayed time reversal,charge conjugation(■)principle to the usual KP equation.Based on the dependent variable transformation,the bilinear form of the AB-KP system is constructed.Explicit trigonometric-hyperbolic,rational and rational-hyperbolic solutions are presented by taking advantage of the Hirota bilinear method.The obtained breather,lump,and interaction solutions enrich the solution structure of nonlocal nonlinear systems.The three-dimensional graphs of these nonlinear wave solutions are demonstrated by choosing the specific parameters.展开更多
文摘In this paper, we propose a numerical method based on semi-Lagrangian approach for solving quasi-geostrophic (QG) equations on a sphere. Using potential vorticity and stream-function as prognostic variables, two-order centered difference is suggested on the latitude-longitude grid. In our proposed numerical scheme, advection terms are expressed in a Lagrangian frame of reference to circumvent the CFL restriction. The pole singularity associated with the latitude-longitude grid is eliminated by a smoothing technique for the initial flow. Error analysis is provided for the numerical scheme.
基金supported by the National Natural Science Foundation of China under grant number 11447017。
文摘A new high-dimensional two-place Alice–Bob-Kadomtsev–Petviashvili(AB-KP)equation is proposed by applying the Alice–Bob-Bob–Alice principle and shifted-parity,delayed time reversal,charge conjugation(■)principle to the usual KP equation.Based on the dependent variable transformation,the bilinear form of the AB-KP system is constructed.Explicit trigonometric-hyperbolic,rational and rational-hyperbolic solutions are presented by taking advantage of the Hirota bilinear method.The obtained breather,lump,and interaction solutions enrich the solution structure of nonlocal nonlinear systems.The three-dimensional graphs of these nonlinear wave solutions are demonstrated by choosing the specific parameters.
