Generalized solitary waves in a finite‐difference Korteweg‐de Vries equation
Generalized solitary waves in a finite‐difference Korteweg‐de Vries equation
复制标题
有限差分 Korteweg-de Vries 方程中的广义孤立波
DOI：
--
复制
发表时间：
2018
期刊：
影响因子：
--
通讯作者：
C. Lustri
中科院分区：
文献类型：
--
作者：
Nalini Joshi;C. Lustri
在一系列奇摄动微分方程中，包括高阶Korteweg‐de弗里斯（KdV）方程，研究了具有指数小非衰减远场振荡的广义孤立波。这些研究中的许多使用指数渐近来计算振荡的行为，揭示了它们在溶液中出现为称为斯托克斯线的特殊曲线交叉。最近的研究发现，差分方程的解也有类似的行为。受这些研究的启发，我们研究了七阶KdV和高阶KdV方程族，确定了产生广义孤立波解的条件。这些结果构成了研究无限阶微分方程的基础，这些微分方程被用作研究格方程的模型。最后，使用有限差分离散化生成格点KdV方程，其中找到格点广义孤立波解。
Generalized solitary waves with exponentially small nondecaying far field oscillations have been studied in a range of singularly perturbed differential equations, including higher order Korteweg‐de Vries (KdV) equations. Many of these studies used exponential asymptotics to compute the behavior of the oscillations, revealing that they appear in the solution as special curves known as Stokes lines are crossed. Recent studies have identified similar behavior in solutions to difference equations. Motivated by these studies, the seventh‐order KdV and a hierarchy of higher order KdV equations are investigated, identifying conditions which produce generalized solitary wave solutions. These results form a foundation for the study of infinite‐order differential equations, which are used as a model for studying lattice equations. Finally, a lattice KdV equation is generated using finite‐difference discretization, in which a lattice generalized solitary wave solution is found.