scholarly journals General multi-linear variable separation approach to solving low dimensional nonlinear systems and localized exitations

2006 ◽  
Vol 55 (3) ◽  
pp. 1011
Author(s):  
Shen Shou-Feng
Keyword(s):  
Nonlinear Systems ◽  
Variable Separation ◽  
Low Dimensional ◽  
Variable Separation Approach

Variable Separation Approach to Solve Nonlinear Systems

2004 ◽  
Vol 42 (4) ◽  
pp. 565-567 ◽  
Author(s):  
Shen Shou-Feng ◽  
Pan Zu-Liang ◽  
Zhang Jun
Keyword(s):  
Nonlinear Systems ◽  
Variable Separation ◽  
Variable Separation Approach

Two-Run Genetic Programming for Predicting Slump Flow of Concrete

2014 ◽  
Vol 590 ◽  
pp. 321-325
Author(s):  
Li Chen ◽  
Chang Huan Kou ◽  
Kuan Ting Chen ◽  
Shih Wei Ma
Keyword(s):  
Nonlinear Systems ◽  
Genetic Programming ◽  
High Performance ◽  
Mean Squared Error ◽  
High Performance Concrete ◽  
Local Optimum ◽  
Root Mean Squared Error ◽  
Squared Error ◽  
Slump Flow ◽  
Low Dimensional

A two-run genetic programming (GP) is proposed to estimate the slump flow of high-performance concrete (HPC) using several significant concrete ingredients in this study. GP optimizes functions and their associated coefficients simultaneously and is suitable to automatically discover relationships between nonlinear systems. Basic-GP usually suffers from premature convergence, which cannot acquire satisfying solutions and show satisfied performance only on low dimensional problems. Therefore it was improved by an automatically incremental procedure to improve the search ability and avoid local optimum. The results demonstrated that two-run GP generates an accurate formula through and has 7.5 % improvement on root mean squared error (RMSE) for predicting the slump flow of HPC than Basic-GP.

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.

Exact Solutions and Solitons with Fission and Fusion Properties for the Generalized Broer-Kaup System

2006 ◽  
Vol 61 (1-2) ◽  
pp. 16-22
Author(s):  
Chun-Long Zheng ◽  
Jian-Ping Fang
Keyword(s):  
Exact Solutions ◽  
Variable Separation ◽  
Soliton Fission ◽  
Dimensional Soliton ◽  
Variable Separation Approach ◽  
03.65 Ge

Starting from a Painlev´e-B¨acklund transformation and a linear variable separation approach, we obtain a quite general variable separation excitation to the generalized (2+1)-dimensional Broer-Kaup (GBK) system. Then based on the derived solution, we reveal soliton fission and fusion phenomena in the (2+1)-dimensional soliton system. - PACS numbers: 05.45.Yv, 03.65.Ge

New Non-Travelling Wave Solutions of Calogero Equation

2016 ◽  
Vol 8 (6) ◽  
pp. 1036-1049 ◽  
Author(s):  
Xiaoming Peng ◽  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Nonlinear Equations ◽  
Symbolic Computation ◽  
Travelling Wave ◽  
Explicit Solutions ◽  
Travelling Wave Solutions ◽  
Variable Separation ◽  
Test Technique ◽  
Reduced Equations ◽  
Wave Solutions ◽  
Variable Separation Approach

AbstractIn this paper, the idea of a combination of variable separation approach and the extended homoclinic test approach is proposed to seek non-travelling wave solutions of Calogero equation. The equation is reduced to some (1+1)-dimensional nonlinear equations by applying the variable separation approach and solves reduced equations with the extended homoclinic test technique. Based on this idea and with the aid of symbolic computation, some new explicit solutions can be obtained.

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.

Variable separation approach by means of the mapping method

2007 ◽  
Vol 75 (4) ◽  
pp. 395-400 ◽  
Author(s):  
Zhi-yun Wang ◽  
Pei-jie Chen ◽  
Chao-qing Dai
Keyword(s):  
Mapping Method ◽  
Variable Separation ◽  
Variable Separation Approach

scholarly journals Time Evolution of Folded (2+1)-Dimensional Solitary Waves

2009 ◽  
Vol 64 (5-6) ◽  
pp. 309-314 ◽  
Author(s):  
Song-Hua Ma ◽  
Yi-Pin Lu ◽  
Jian-Ping Fang ◽  
Zhi-Jie Lv
Keyword(s):  
Solitary Wave ◽  
Elliptic Function ◽  
Water Wave ◽  
Periodic Wave ◽  
Wave System ◽  
Solitary Wave Solutions ◽  
Variable Separation ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Variable Separation Approach

Abstract With an extended mapping approach and a linear variable separation approach, a series of solutions (including theWeierstrass elliptic function solutions, solitary wave solutions, periodic wave solutions and rational function solutions) of the (2+1)-dimensional modified dispersive water-wave system (MDWW) is derived. Based on the derived solutions and using some multi-valued functions, we find a few new folded solitary wave excitations.

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