In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectra...In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes areproposed, the convergence and stability for the schemes are proved.展开更多
In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic ...In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.展开更多
文摘In this paper, the following generalized KdV equations with periodic initialvalue problem is considered:u→t + (gradψ(u→))x + u→xxx - αu→xx + γu→ = f→(x, t, u→)semi-discrete and fully discrete Fourier spectral and pseudo-spectral schemes areproposed, the convergence and stability for the schemes are proved.
文摘In this paper, generalized KdV equations are investigated by using a mathematical technique based on the reduction of order for solving differential equations. The compactons, solitons, solitary patterns and periodic solutions for the equations presented in this paper are obtained. For these generalized KdV equations, it is found that the change of the exponents of the wave function u and the coefficient a, positive or negative, leads to the different physical structures of the solutions.
