New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s pa...New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.展开更多
本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^...本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.展开更多
In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation i...In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions or the numerical solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show the efficiency of the method computationally.展开更多
文摘New exact solutions, expressed in terms of the Jacobi elliptic functions, to the nonlinear Klein-Gordon equation are obtained by using a modified mapping method. The solutions include the conditions for equation＇s parameters and travelling wave transformation parameters. Some figures for a specific kind of solution are also presented.
文摘本文讨论非线性Klein-Gordon 方程的混合问题{u(■)—△u+u=F(u,Du,D_xDu) (t,x)∈(0,T)×Ωu(0,x)=h(x) u_t(0,x)=g(x),x∈Ω■u/■v=0■在F(u,Du,D_xDu)≥p sum from i=1 to n u_(X_i)~2+qu_t^2+u 这里(p>0,q>0) 及■_■■^(ph)(x)×g(x)dx>0时,得到该问题的解在有限时间内爆破.
文摘In this paper, in order to extend the lattice Boltzmann method to deal with more nonlinear equations, a one-dimensional (1D) lattice Boltzmann scheme with an amending function for the nonlinear Klein-Gordon equation is proposed. With the Taylor and Chapman-Enskog expansion, the nonlinear Klein-Gordon equation is recovered correctly from the lattice Boltzmann equation. The method is applied on some test examples, and the numerical results have been compared with the analytical solutions or the numerical solutions reported in previous studies. The L2, L∞ and Root-Mean-Square (RMS) errors in the solutions show the efficiency of the method computationally.
