scholarly journals Novel Soliton Molecules and Wave Interactions for A (3+1)-Dimensional Nonlinear Evolutionary Equation

2021 ◽  
Author(s):  
Xiaoyan Tang ◽  
Chao Jie Cui ◽  
Zu feng Liang ◽  
Wei Ding
Keyword(s):  
Nonlinear Evolution ◽  
Evolutionary Equation ◽  
New Wave ◽  
Variable Separation ◽  
Wave Interactions ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Soliton Lattice ◽  
Wave Patterns ◽  
Nonlinear Evolutionary Equation

Abstract New wave excitations are revealed for a (3+1)-dimensional nonlinear evolution equation to enrich nonlinear wave patterns in nonlinear systems. Based on a new variable separation solution with two arbitrary variable separated functions obtained by means of the multilinear variable separation approach, localized excitations of N dromions, N x M lump lattice and N x M ring soliton lattice are explored. Interestingly, it is observed that soliton molecules can be composed of diverse "atoms" such as the dromions, lumps and ring solitons, respectively. Elastic interactions between solitons and soliton molecules are graphically demonstrated.

Variable Separation Approach for the Sine-Gordon System

2004 ◽  
Vol 59 (10) ◽  
pp. 629-634 ◽  
Author(s):  
Xian-jing Lai ◽  
Jie-fang Zhang
Keyword(s):  
Solitary Waves ◽  
Periodic Waves ◽  
Variable Separation ◽  
Elastic Interactions ◽  
Localized Excitations ◽  
Variable Separation Approach

Using the B¨acklund transformation and a variable separation approach with some arbitrary functions, three new types of solutions of the sine-Gordon system have been obtained. The excitations are localized as well as non-localized. E.g. solitoffs, dromions, multidromions, lumps, breathers, instantons, multivalued solitary waves, doubly periodic waves, etc., can be constructed on the basis of selecting the arbitrary functions properly. Also the interaction properties for all the possible localized excitations are of interest. In this paper, we discuss two elastic interactions. - PACS Ref: 05.45.Yv, 02.30.Jr, 02.30.Ik.

Exact Solutions and Localized Excitations of Burgers System in (3+1) Dimensions

2011 ◽  
Vol 66 (6-7) ◽  
pp. 383-391 ◽  
Author(s):  
Chun-Long Zheng ◽  
Hai-Ping Zhu
Keyword(s):  
Linear System ◽  
Exact Solutions ◽  
The Novel ◽  
Variable Separation ◽  
Linear Superposition ◽  
Localized Excitations ◽  
New Type ◽  
Superposition Theorem ◽  
Burgers System

With the help of a Cole-Hopf transformation, the nonlinear Burgers system in (3+1) dimensions is reduced to a linear system. Then by means of the linear superposition theorem, a general variable separation solution to the Burgers system is obtained. Finally, based on the derived solution, a new type of localized structure, i.e., a solitonic bubble is revealed and some evolutional properties of the novel localized structure are briefly discussed

scholarly journals Regarding New Wave Patterns of the Newly Extended Nonlinear (2+1)-Dimensional Boussinesq Equation with Fourth Order

Mathematics ◽  
2020 ◽  
Vol 8 (3) ◽  
pp. 341 ◽  
Author(s):  
Juan Luis García Guirao ◽  
Haci Mehmet Baskonus ◽  
Ajay Kumar
Keyword(s):  
Fourth Order ◽  
Boussinesq Equation ◽  
Soliton Solutions ◽  
Expansion Method ◽  
Bright Soliton ◽  
New Wave ◽  
Wave Patterns

This paper applies the sine-Gordon expansion method to the extended nonlinear (2+1)-dimensional Boussinesq equation. Many new dark, complex and mixed dark-bright soliton solutions of the governing model are derived. Moreover, for better understanding of the results, 2D, 3D and contour graphs under the strain conditions and the suitable values of parameters are also plotted.

Localized Excitations in a Dispersive Long Water-Wave System via an Extended Projective Approach

2007 ◽  
Vol 62 (3-4) ◽  
pp. 140-146 ◽  
Author(s):  
Jin-Xi Fei ◽  
Chun-Long Zheng
Keyword(s):  
Coherent Structures ◽  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Localized Excitations ◽  
Complex Wave ◽  
New Type ◽  
03.65 Ge

By means of an extended projective approach, a new type of variable separation excitation with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Based on the derived variable separation excitation, abundant localized coherent structures such as single-valued localized excitations, multiple-valued localized excitations and complex wave excitations are revealed by prescribing appropriate functions. - PACS numbers: 03.65.Ge, 05.45.Yv

Multi-Soliton Excitations and Chaotic Patterns for the (2+1)-Dimensional Breaking-Soliton System

2010 ◽  
Vol 65 (6-7) ◽  
pp. 477-482 ◽  
Author(s):  
Li-Chen Lü ◽  
Song-Hua Ma ◽  
Jian-Ping Fang
Keyword(s):  
Solitary Wave ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Wave Solutions ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from a projective equation and a linear variable separation approach, some solitary wave solutions with arbitrary functions for the (2+1)-dimensional breaking soliton system are derived. Based on the derived solution and by selecting appropriate functions, some novel localized excitations such as multi-solitons and chaotic-solitons are investigated.

Application of the Improved Mapping Approach to Exact Solutions and Chaotic Patterns for a Nonlinear Equation

2014 ◽  
Vol 945-949 ◽  
pp. 2430-2434
Author(s):  
Yan Lei ◽  
Song Hua Ma ◽  
Jian Ping Fang
Keyword(s):  
Nonlinear Equation ◽  
Exact Solutions ◽  
Variable Separation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
Variable Separation Approach

Starting from an improved mapping approach and a linear variable separation approach, a series of exact solutions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli system (BLMP) is derived. Based on the derived variable separated solution, we obtain some special localized excitations such as dromion, solitoff and chaotic patterns.

scholarly journals The Global Existence of Nonlinear Evolutionary Equation with Small Delay

2012 ◽  
Vol 2012 ◽  
pp. 1-10
Author(s):  
Xunwu Yin
Keyword(s):  
Global Existence ◽  
Local Existence ◽  
Evolutionary Equation ◽  
Fractional Powers ◽  
Gronwall’S Inequality ◽  
Sectorial Operators ◽  
Local Existence And Uniqueness ◽  
Small Delay ◽  
Fixed Point Principle ◽  
Nonlinear Evolutionary Equation

We investigate the global existence of the delayed nonlinear evolutionary equation∂tu+Au=f(u(t),u(t−τ)). Our work space is the fractional powers spaceXα. Under the fundamental theorem on sectorial operators, we make use of the fixed-point principle to prove the local existence and uniqueness theorem. Then, the global existence is obtained by Gronwall’s inequality.

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