Parra Prado Hugo, Cisneros-Ake Luis A
Posgrado en Ciencias Fisicomatemáticas, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 Cd. de México, Mexico.
Departamento de Matemáticas, ESFM, Instituto Politécnico Nacional, Unidad Profesional Adolfo López Mateos Edificio 9, 07738 Cd. de México, Mexico.
Chaos. 2019 May;29(5):053133. doi: 10.1063/1.5092985.
The Hirota bilinear method is extended to find one- and two-hump exact bright and dark soliton solutions to a coupled system between the linear Schrödinger and Korteweg-de Vries (KdV) equations arising in the energy transfer problem along a cubic anharmonic crystal medium. The bilinear form associated to this system is found by imitating the well known bilinearizing transformations used in the standard nonlinear Schrödinger (NLS) and KdV equations. Proper finite exponential expansions in the transformed variables allow one to exhibit multihump soliton solutions as single entities resulting from the adjustment of appropriate dispersion relations between the wave parameters describing the profiles. It is found that such one- and two-hump solutions correspond to the one- and two-KdV solitons trapped by both the bright and dark-gray NLS solitons. Our two-hump bright and dark solutions represent novel solutions for the type of interactions and nonlinearities considered.
广田双线性方法得到扩展，用于求解一个耦合系统的单峰和双峰精确亮孤子与暗孤子解，该耦合系统由沿立方非谐晶体介质的能量转移问题中产生的线性薛定谔方程和科特韦格 - 德弗里斯（KdV）方程组成。通过模仿标准非线性薛定谔（NLS）方程和KdV方程中使用的著名双线性化变换，找到与该系统相关的双线性形式。在变换变量中进行适当的有限指数展开，使人们能够将多峰孤子解展示为单个实体，这是通过调整描述波形的波参数之间的适当色散关系而得到的。结果发现，这种单峰和双峰解对应于被亮和暗灰色NLS孤子捕获的单KdV孤子和双KdV孤子。我们的双峰亮孤子和暗孤子解代表了所考虑的相互作用和非线性类型的新解。
