We show that a direct perturbation theory can be used to give a systematic description of the evolution of breather in perturbed sine-Gordon equation. The error in inverse scattering method is also pointed out and cor...We show that a direct perturbation theory can be used to give a systematic description of the evolution of breather in perturbed sine-Gordon equation. The error in inverse scattering method is also pointed out and corrected to obtain the accurate results.展开更多
We construct a Hartree-Fock (self-consistent)-like algorithm with renormalization group (RG) approach to calculate the anomalous dimension in a nonlinear diffusion equation. We find that our result improves the origin...We construct a Hartree-Fock (self-consistent)-like algorithm with renormalization group (RG) approach to calculate the anomalous dimension in a nonlinear diffusion equation. We find that our result improves the original RG work because we include the effect of Heaviside function.展开更多
A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization grou...A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.展开更多
文摘We show that a direct perturbation theory can be used to give a systematic description of the evolution of breather in perturbed sine-Gordon equation. The error in inverse scattering method is also pointed out and corrected to obtain the accurate results.
文摘We construct a Hartree-Fock (self-consistent)-like algorithm with renormalization group (RG) approach to calculate the anomalous dimension in a nonlinear diffusion equation. We find that our result improves the original RG work because we include the effect of Heaviside function.
文摘A new method - perturbative summation to infinite order is presented to obtain the anomalous dimension in the solution of the modified porous medium equation. The result is the same as that in the renormalization group (RG) approach. It gives us an insight into the anomalous exponent in the asymptotic solution of the modified porous medium equation in the RG approach. Based on this discussion, we can see that the anomalous dimension appears naturally in the problem and the nonlinearity reflects the anomalous long-time behavior of the system.
