平顶孤子：扩展Gardner方程中的平顶孤子
Flatons: flat-top solitons in extended Gardner equations
摘要：
在Gardner方程及其扩展中，非凸对流限制了孤子/孤子速度的范围，超过该范围，孤子/孤子速度溶解并形成扭结/反扭结。靠近孤子势垒，我们展开一个狭窄的速度带，在那里孤子的形状经历了结构性的变化，而不是随着速度的增长，它们的顶部弯曲，它们迅速加宽;速度的$ε^2 << 1$变化导致它们的宽度扩展ln $(1/ ε)$。这些孤立波，称为平子，可以很好地近似看作是由彼此之间任意距离的扭结和反扭结组成的。像普通的孤子一样，一旦形成平子，它们就非常健壮。加德纳方程的多维扩展表明，球形平子是普遍存在的，在许多情况下，每个允许的速度支持一个完整的序列的多节平子。
英文摘要：
In both the Gardner equation and its extensions, the non-convex convection bounds the range of solitons / compactons velocities beyond which they dissolve and kink/anti-kink form. Close to solitons barrier we unfold a narrow strip of velocities where solitons shape undergoes a structural change and rather than grow with velocity, their top flattens and they widen rapidly; $ε^2 << 1$ change in velocity causes their width to expand ln $(1/ ε)$. To a very good approximation these solitary waves, referred to as flatons, may be viewed as made of a kink and anti-kink placed at an arbitrary distance from each other. Like ordinary solitons, once flatons form they are very robust. A multi-dimensional extension of the Gardner equation reveals that spherical flatons are as prevalent and in many cases every admissible velocity supports an entire sequence of multi-nodal flatons.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
