High-order breathers, lumps, and semi-rational solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equation
High-order breathers, lumps, and semi-rational solutions to the (2+1)-dimensional Hirota-Satsuma-Ito equation
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(2 1) 维 Hirota-Satsuma-Ito 方程的高阶呼吸、块和半有理解
DOI：
10.1088/1402-4896/ab04bb
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发表时间：
2019
期刊：
影响因子：
2.9
通讯作者：
Zheng Xiaoxiao
中科院分区：
文献类型：
--
作者：
Liu Wei;Wazwaz Abdul-Majid;Zheng Xiaoxiao
这项工作正在研究 (2+1) 维 Hirota-Satsuma-Ito (HSI) 方程。通过使用贝尔多项式，简洁地获得了 HSI 方程的双线性形式。借助所获得的双线性形式，我们首先利用 Hirota 双线性方法结合微扰展开构造一般高阶孤子解。通过取高阶孤子解的特定复共轭条件，简洁地导出了高阶呼吸器解以及由呼吸器和线孤子组成的混合解。我们通过采用长波极限进一步生成称为高阶块的有理解。最后，我们研究了两种类型的半有理解，它们描述了块与线孤子之间或块与呼吸器之间的相互作用。这些碰撞是弹性的，相互作用后不会导致振幅、速度以及线孤子、呼吸子和团块的形状发生任何变化。
Under investigation in this work is the (2+ 1)-dimensional Hirota–Satsuma–Ito (HSI) equation. By employing Bell's polynomials, bilinear formalism of the HSI equation is succinctly obtained. With the aid of the obtained bilinear formalism, we first construct general high-order soliton solutions by using Hirota's bilinear method combined with the perturbation expansion. By taking particular complex conjugate conditions of the high-order soliton solutions, high-order breather solutions and the mixed solutions consisting of breathers and line solitons are succinctly derived. We further generate rational solutions termed high-order lumps by taking a long wave limit. Finally, we investigate two types of semi-rational solutions, which describe interaction between lumps and line solitons, or between lumps and breathers. These collisions are elastic, which do not lead to any changes of amplitudes and velocities, and shapes of the line solitons, breathers and lumps after interaction.