Ankiewicz Adrian, Akhmediev Nail, Soto-Crespo J M
The Australian National University, Canberra, Australian Capital Territory 0200, Australia.
Phys Rev E Stat Nonlin Soft Matter Phys. 2010 Aug;82(2 Pt 2):026602. doi: 10.1103/PhysRevE.82.026602. Epub 2010 Aug 11.
We show that the Ablowitz-Ladik equation, which is an integrable form of the discretized nonlinear Schrödinger equation, has rogue wave solutions in the form of the rational solutions. We show that there is a hierarchy of rational solutions and we derive the two lowest-order ones using the Hirota technique. More generally, we present rational solutions for the discrete Hirota equation which includes, as particular cases, both the discrete Ablowitz-Ladik equation and the discrete modified Korteweg-de Vries (mKdV) equation.
我们证明，作为离散非线性薛定谔方程的可积形式的阿布洛维茨－拉迪克方程具有有理函数形式的 rogue 波解。我们证明存在一个有理函数解的层级结构，并使用广田技术推导出两个最低阶的解。更一般地，我们给出了离散广田方程的有理函数解，作为特殊情况，该方程包括离散阿布洛维茨－拉迪克方程和离散修正科特韦格－德弗里斯（mKdV）方程。
