SINGLE AND MULTIPLE VALUED LOCALIZED EXCITATIONS OF BOITI-LEON-PEMPINELLI SYSTEM IN (2+1)-DIMENSIONS VIA A MAPPING METHOD

2006 ◽  
Vol 20 (22) ◽  
pp. 3233-3245 ◽  
Author(s):  
CHUN-LONG ZHENG ◽  
HAI-PING ZHU ◽  
LIN-SEN XIE ◽  
JIAN-PING FANG
Keyword(s):  
Initial Conditions ◽  
Mapping Method ◽  
Variable Separation ◽  
Mapping Approach ◽  
Localized Excitations ◽  
New Type

With the help of a mapping approach, a new type of variable separation solution with two arbitrary functions to (2+1)-dimensional Boiti–Leon–Pempinelli system (BLP) is derived. Based on the derived variable separation solution, some single valued and multiple valued localized excitations such as dromions, peakons and foldons, etc. with novel evolutional properties are revealed by introducing appropriate initial conditions in this paper.

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

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

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.

Bell-Like and Peak-Like Loop Solitons in (2+1)-Dimensional Dispersive Long Water-Wave System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 39-44
Author(s):  
Hai-Ping Zhu ◽  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Water Wave ◽  
Wave System ◽  
Variable Separation ◽  
Mapping Approach ◽  
New Type ◽  
Extended Mapping ◽  
03.65 Ge

Starting from an extended mapping approach, a new type of variable separation solution with arbitrary functions of the (2+1)-dimensional dispersive long water-wave (DLW) system is derived. Then based on the derived solution, we reveal some new types of loop solitons such as bell-like loop solitons and peak-like loop solitons in the (2+1)-dimensional DLW system. - PACS numbers: 05.45.Yv, 03.65.Ge

New Variable Separation Excitations of a (2+1)-Dimensional Broer-Kaup-Kupershmidt System Obtained by an Extended Mapping Approach

2004 ◽  
Vol 59 (12) ◽  
pp. 912-918 ◽  
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang ◽  
Li-Qun Chen
Keyword(s):  
Variable Separation ◽  
Mapping Approach ◽  
New Type ◽  
Extended Mapping ◽  
03.65 Ge

Using an extended mapping approach, a new type of variable separation excitation with two arbitrary functions of the (2+1)-dimensional Broer-Kaup-Kupershmidt system (BKK) is derived. Based on this excitation, abundant propagating and non-propagating solitons, such as dromions, rings, peakons, compactons, etc. are found by selecting appropriate functions. - PACS: 05.45.Yv, 03.65.Ge

COMPUTATIONAL STUDIES OF DISCRETE BREATHERS — FROM BASICS TO COMPETING LENGTH SCALES

2006 ◽  
Vol 16 (06) ◽  
pp. 1645-1669 ◽  
Author(s):  
SERGEJ FLACH ◽  
ANDREY GORBACH
Keyword(s):  
Initial Conditions ◽  
Computational Studies ◽  
Machine Precision ◽  
Algebraic Decay ◽  
Computational Tools ◽  
Length Scales ◽  
Localized Excitations ◽  
Long Range Interactions ◽  
Discrete Breathers ◽  
Anharmonic Interactions

This work provides a description of the main computational tools for the study of discrete breathers. It starts with the observation of breathers through simple numerical runs, the study uses targeted initial conditions, and discrete breather impact on transient processes and thermal equilibrium. We briefly describe a set of numerical methods to obtain breathers up to machine precision. In the final part of this work we apply the discussed methods to study the competing length scales for breathers with purely anharmonic interactions — favoring superexponential localization — and long range interactions, which favor algebraic decay in space. As a result, we observe and explain the presence of three different spatial tail characteristics of the considered localized excitations.

Difference Synchronization of Identical and Nonidentical Chaotic and Hyperchaotic Systems of Different Orders Using Active Backstepping Design

2018 ◽  
Vol 13 (5) ◽  
Author(s):  
Eric Donald Dongmo ◽  
Kayode Stephen Ojo ◽  
Paul Woafo ◽  
Abdulahi Ndzi Njah
Keyword(s):  
Chaotic System ◽  
Initial Conditions ◽  
Lyapunov Stability Theory ◽  
The State ◽  
State Variables ◽  
State Variable ◽  
New Type ◽  
The Difference ◽  
Synchronization Scheme ◽  
Hyperchaotic Systems

This paper introduces a new type of synchronization scheme, referred to as difference synchronization scheme, wherein the difference between the state variables of two master [slave] systems synchronizes with the state variable of a single slave [master] system. Using the Lyapunov stability theory and the active backstepping technique, controllers are derived to achieve the difference synchronization of three identical hyperchaotic Liu systems evolving from different initial conditions, as well as the difference synchronization of three nonidentical systems of different orders, comprising the 3D Lorenz chaotic system, 3D Chen chaotic system, and the 4D hyperchaotic Liu system. Numerical simulations are presented to demonstrate the validity and feasibility of the theoretical analysis. The development of difference synchronization scheme has increases the number of existing chaos synchronization scheme.

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.

The Homotopy-Perturbation Method for Solving Klein-Gordon-Type Equations with Unbounded Right- Hand Side

2009 ◽  
Vol 64 (1-2) ◽  
pp. 149-152 ◽  
Author(s):  
Afgan Aslanov
Keyword(s):  
Perturbation Method ◽  
Exact Solutions ◽  
Homotopy Perturbation Method ◽  
Initial Conditions ◽  
Homotopy Perturbation ◽  
Right Hand ◽  
Klein Gordon ◽  
New Type ◽  
Solvable Problems

The approximate and/or exact solutions of the generalized Klein-Gordon- and sine-Gordon-type equations are obtained. We introduce a new type of initial conditions to extend the class of solvable problems

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