Rational solutions and lump solutions to the (3+1)-dimensional Mel'nikov equation

被引：4

作者：

Yong, Xuelin ^{[1
]}

Li, Xiaoyu ^{[1
]}

Huang, Yehui ^{[1
]}

Ma, Wen-Xiu ^{[2
,3
,4
,5
,6
]}

Liu, Yong ^{[7
]}

机构：

[1] North China Elect Power Univ, Sch Math Sci & Phys, Beijing 102206, Peoples R China

[2] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China

[3] Univ S Florida, Dept Math & Stat, Tampa, FL 33620 USA

[4] North West Univ, Dept Math Sci, Mafikeng Campus,Private Bag X 2046, ZA-2735 Mmabatho, South Africa

[5] Shandong Univ Sci & Technol, Coll Math & Syst Sci, Qingdao 266590, Shandong, Peoples R China

[6] King Abdulaziz Univ, Dept Math, Jeddah, Saudi Arabia

[7] Univ Sci & Technol China, Sch Math Sci, Hefei 230026, Anhui, Peoples R China

来源：

MODERN PHYSICS LETTERS B | 2020年 / 34卷 / 03期

关键词：

Rational solutions; lump solutions; Mel'nikov equation; Hirota bilinear method; SELF-CONSISTENT SOURCES; GROSS-PITAEVSKII EQUATION; SOLITON-SOLUTIONS; KINK SOLUTIONS; KP EQUATION; CONSTRUCTION; HIERARCHY; DYNAMICS; WAVES;

D O I：

10.1142/S0217984920500335

中图分类号：

O59 [应用物理学];

学科分类号：

摘要：

In this paper, explicit representation of general rational solutions for the (3 + 1)-dimensional Mel'nikov equation is derived by employing the Hirota bilinear method. It is obtained in terms of determinants whose matrix elements satisfy some differential and difference relations. By selecting special value of the parameters involved, the first-order and second-order lump solutions are given and their dynamic characteristics are illustrated by two- and three-dimensional figures.

引用

页数：14

共 48 条

[1]

[Anonymous], 1991, Nonlinear evolution equations and inverse scattering

[2] A study of lump-type and interaction solutions to a (3+1)-dimensional Jimbo-Miwa-like equation [J].

Batwa, Sumayah ;

Ma, Wen-Xiu .

COMPUTERS & MATHEMATICS WITH APPLICATIONS, 2018, 76 (07) :1576-1582

[3]

Bluman GW, 2002, Symmetry and Integration Methods for Differential Equations

[4]

Chen DY., 2006, Introduction to soliton theory

[5] The multisoliton solutions of the KP equation with self-consistent sources [J].

Deng, SF ;

Chen, DY ;

Zhang, DJ .

JOURNAL OF THE PHYSICAL SOCIETY OF JAPAN, 2003, 72 (09) :2184-2192

[6]

ENNS RH, 1981, NONLINEAR PHENOMENA

[7] Lump solution and its interaction to (3+1)-D potential-YTSF equation [J].

Foroutan, Mohammadreza ;

Manafian, Jalil ;

Ranjbaran, Arash .

NONLINEAR DYNAMICS, 2018, 92 (04) :2077-2092

[8]

Gu C., 2004, Darboux Transformations in Integrable Systems Theory and their Applications to Geometry

[9]

Hirota R., 2004, The direct method in soliton theory, V155

[10] New type of Kadomtsev-Petviashvili equation with self-consistent sources and its bilinear Backlund transformation [J].

Hu, Xing-Biao ;

Wang, Hong-Yan .

INVERSE PROBLEMS, 2007, 23 (04) :1433-1444

← 1 2 3 4 5 →