Symplectic computation of solitary waves for general Sine–Gordon equations

A Fourth-Order Compact Finite Volume Scheme for 1D Sine-Gordon Equations

“…一维 Sine-Gordon 方程是重要的非线性数学物理方程，可以用来描述流体力学、气象学、场论等领域 很多物理现象。例如，传播中的磁通量子两个超导体之间的约瑟夫逊结 [1]，严格的钟摆的运动在拉伸线 [2]、固体物理、非线性光学、流体运动的稳定性。人们对此已经用一些方法作了研究。例如，显式有限 差分格式和隐格式离散能量守恒方法 [3]。Strauss and Vázquez [4]，使用经典的有限差分格式 [5] [6]，计算 了 Klein-Gordon 方程。 而 [7]的作者提出了一个使用基函数的方法。 Ramos [8]使用五点隐式有限差分方法。 [9]提出了一种通用的解决 Sine-Gordon 方程的辛方法。Batiha et al [ ,0 , ,0 , ,…”

The boundary integral equation approach for numerical solution of the one‐dimensional Sine‐Gordon equation

“…In this example, we consider the motion of double kinks in the SG equation. The analytic form of the double kinks in the SG equation can be expressed as [13]:…”

“…Wei [12] investigated the utility of a discrete singular convolution algorithm for the integration of the SG equation. Lu [13] presented a class of symplectic schemes for the computation of solutions of the general SG systems. Wazwaz employed the tanh method and a variable separated ODE method for solving the double SG equation [1] and the reliable tanh method to handle the generalized SG and the generalized sinh−Gordon equations [14].…”

Multilevel augmentation methods for solving the sine-Gordon equation

“…[3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20][21][22]). Specifically, readers can refer to [8,17,19] for finite difference schemes, [4,5] for finite element methods, [11,20,21] for energy conserving schemes, and [16,18] for symplectic algorithms. Recently, some other methods are applied to solving the equation such as the modified Adomian decomposition method (cf.…”