In this paper we study dispersive enhancement of a wave train in systems described by the fractional Korteweg–de Vries-type equations of the form ##IMG## [http://ej.iop.org/images/1751-8121/53/34/345703/aab9da3ieqn1.gif] {${u}_{t}+{\alpha }_{n}\enspace {u}^{n}\enspace {u}_{x}+{\beta }_{m}{\left({D}_{m}\left\{u\right\}\right)}_{x}=0,{D}_{m}\left\{u\right\}=-\vert k{\vert }^{m}\enspace u\left(k\right)$} where the operator D m { u } is written in the Fourier space, α n , β m are arbitrary constants and n , m being rational numbers (positive or negative). Using both approximate and exact solutions of these wave equations we describe constructively the process of dispersive focusing. It is based on a time-reversing approach with the expected rogue wave chosen as the initial condition for a solution of these equations. We demonstrate the qualitative difference in the ...

中文翻译：

---

分数Korteweg-de Vries型方程的色散聚焦

在本文中，我们研究由分数Korteweg-de Vries型方程以## IMG ##形式描述的系统中波列的色散增强[http://ej.iop.org/images/1751-8121/53 /34/345703/aab9da3ieqn1.gif] {$ {u} _ {t} + {\ alpha} _ {n} \ enspace {u} ^ {n} \ enspace {u} _ {x} + {\ beta} _ {m} {\ left（{D} _ {m} \ left \ {u \ right \} \ right）} _ {x} = 0，{D} _ {m} \ left \ {u \ right \ } =-\ vert k {\ vert} ^ {m} \ enspace u \ left（k \ right）$}其中，运算符D m {u}写在傅立叶空间中，αn，βm是任意常数，并且n，m是有理数（正数或负数）。使用这些波动方程的近似解和精确解，我们可以建设性地描述色散聚焦的过程。它基于时间反转方法，其中预期的流氓波被选择为这些方程式求解的初始条件。