Families of Rational and Semirational Solutions of the Partial Reverse Space-Time Nonlocal Mel'nikov Equation
Families of Rational and Semirational Solutions of the Partial Reverse Space-Time Nonlocal Mel'nikov Equation
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DOI：
10.1155/2020/2642654
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发表时间：
2020
期刊：
影响因子：
2.3
通讯作者：
Lou Senyue
中科院分区：
文献类型：
--
作者：
Liu Wei;Qin Zhenyun;Chow Kwok Wing;Lou Senyue
Exact periodic and localized solutions of a nonlocal Mel′nikov equation are derived by the Hirota bilinear method. Many conventional nonlocal operators involve integration over a spatial or temporal domain. However, the present class of nonlocal equations depends on properties at selected far field points which result in a potential satisfying parity time symmetry. The present system of nonlocal partial differential equations consists of two dependent variables in two spatial dimensions and time, where the dependent variables physically represent a wave packet and an auxiliary scalar field. The periodic solutions may take the forms of breathers (pulsating modes) and line solitons. The localized solutions can include propagating lumps and rogue waves. These nonsingular solutions are obtained by appropriate choice of parameters in the Hirota expansion. Doubly periodic solutions are also computed with elliptic and theta functions. In sharp contrast with the local Mel′nikov equation, the auxiliary scalar field in the present set of solutions can attain complex values. Through a coordinate transformation, the governing equation can reduce to the Schrödinger–Boussinesq system.
