Families of Rational and Semirational Solutions of the Partial Reverse Space-Time Nonlocal Mel'nikov Equation

被引:5
作者
Liu, Wei [1 ]
Qin, Zhenyun [2 ,3 ]
Chow, Kwok Wing [4 ]
Lou, Senyue [5 ]
机构
[1] Shandong Technol & Business Univ, Coll Math & Informat Sci, Yantai 264005, Peoples R China
[2] Fudan Univ, Sch Math, Shanghai 200433, Peoples R China
[3] Fudan Univ, Key Lab Nonlinear Math Models & Methods, Shanghai 200433, Peoples R China
[4] Univ Hong Kong, Dept Mech Engn, Pokfulam, Hong Kong, Peoples R China
[5] Ningbo Univ, Dept Phys, Ningbo, Zhejiang, Peoples R China
基金
上海市自然科学基金; 中国国家自然科学基金;
关键词
TRAVELING-WAVE SOLUTIONS; ROGUE WAVES; DARBOUX TRANSFORMATION; SOLITON-SOLUTIONS;
D O I
10.1155/2020/2642654
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
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 Schrodinger-Boussinesq system.
引用
收藏
页数:18
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