The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. ...The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.展开更多
The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments...The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments show exactly that rogue waves occur in deep and shallow water. To study the behavior of freak waves in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems, we derive a modified nonlinear Schrödinger equation modeling the propagation of rogue waves in deep water in order to seek analytic solutions of this nonlinear partial differential equation by using generalized extended G'/G-expansion method with the aid of mathematica. Particular attentions have been paid to the behavior of rogue wave’s amplitude which highlights rogue wave’s destructive power.展开更多
In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 eq...In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.展开更多
This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal di...This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem(TEVP).To solve the pin-resolved TEVP,VITAS uses a heterogeneous variational nodal method(VNM).The spatial flux is approximated at each Cartesian node using finite elements in the x-y plane and orthogonal polynomials along the z-axis.Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces.To further lower the computational cost,a predictor–corrector quasi-static SCM(PCQ-SCM)was developed.Within the VNM framework,computational models for the adjoint neutron flux and kinetic parameters are presented.The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional(2D)and three-dimensional(3D)exercises on the OECD/NEA C5G7-TD benchmark.In the 2D and 3D problems,the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97%and 1.57%,respectively.In addition,numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps,thereby reducing the computational cost 100-fold,without compromising numerical accuracy.展开更多
基金Project supported by the National Nature Science Foundation of China （Grant No 49894190） of the Chinese Academy of Science （Grant No KZCXI-sw-18）, and Knowledge Innovation Program.
文摘The extended F-expansion method or mapping method is used to construct exact solutions for the coupled KleinGordon Schr/Sdinger equations （K-G-S equations） by the aid of the symbolic computation system Mathematica. More solutions in the Jacobi elliptic function form are obtained, including the single Jacobi elliptic function solutions, combined Jacobi elliptic function solutions, rational solutions, triangular solutions, soliton solutions and combined soliton solutions.
文摘The existence of rogue (or freak) waves is now universally recognized and material proofs on the extent of damage caused by these ocean’s phenomena are available. Marine observations as well as laboratory experiments show exactly that rogue waves occur in deep and shallow water. To study the behavior of freak waves in terms of their space and time evolution, that is, their motion and also in terms of mechanical transformations that these systems may suffer in their dealings with other systems, we derive a modified nonlinear Schrödinger equation modeling the propagation of rogue waves in deep water in order to seek analytic solutions of this nonlinear partial differential equation by using generalized extended G'/G-expansion method with the aid of mathematica. Particular attentions have been paid to the behavior of rogue wave’s amplitude which highlights rogue wave’s destructive power.
文摘In this study, we will introduce the modified (G'/G<sup>2</sup>)-expansion method to explore some of the exact traveling wave solutions of some nonlinear partial differential equations namely, Phi-4 equation, Joseph-Egri (TRLW) equation, and Calogro-Degasperis (CD) equation. As a result, we have obtained solutions for the equations expressed in terms of trigonometric, hyperbolic and rational functions. Moreover, some selected solutions are plotted using some specific values for the parameters.
基金supported by the National Natural Science Foundation of China (Nos. 12175138, U20B2011)the Young Talent Project of the China National Nuclear Corporation
文摘This article describes the transient models of the neutronics code VITAS that are used for solving time-dependent,pinresolved neutron transport equations.VITAS uses the stiffness confinement method(SCM)for temporal discretization to transform the transient equation into the corresponding transient eigenvalue problem(TEVP).To solve the pin-resolved TEVP,VITAS uses a heterogeneous variational nodal method(VNM).The spatial flux is approximated at each Cartesian node using finite elements in the x-y plane and orthogonal polynomials along the z-axis.Angular discretization utilizes the even-parity integral approach at the nodes and spherical harmonic expansions at the interfaces.To further lower the computational cost,a predictor–corrector quasi-static SCM(PCQ-SCM)was developed.Within the VNM framework,computational models for the adjoint neutron flux and kinetic parameters are presented.The direct-SCM and PCQ-SCM were implemented in VITAS and verified using the two-dimensional(2D)and three-dimensional(3D)exercises on the OECD/NEA C5G7-TD benchmark.In the 2D and 3D problems,the discrepancy between the direct-SCM solver’s results and those reported by MPACT and PANDAS-MOC was under 0.97%and 1.57%,respectively.In addition,numerical studies comparing the PCQ-SCM solver to the direct-SCM solver demonstrated that the PCQ-SCM enabled substantially larger time steps,thereby reducing the computational cost 100-fold,without compromising numerical accuracy.
