A few Kinds of Riccati Equation Integrable Conditions and Variable Separation Method

2014 ◽  
Vol 556-562 ◽  
pp. 3642-3647
Author(s):  
Zhi Hong Yin
Keyword(s):  
General Solution ◽  
Riccati Equation ◽  
Integral Form ◽  
Separation Method ◽  
Variable Separation ◽  
Variable Substitution ◽  
Variable Separation Method

Summarizes several types of the Riccati equation can be used in the form of elementary integral form and its general solution. The Riccati equation through the appropriate variable substitution can be variable separable equation, to calculate the general solution to use the method of elementary integrals. Some of these methods need certain skills. With a typical example this paper introduces the basic techniques of variable substitution.

New Variable Separation Solutions in (2+1)-Dimensionals: The Boiti-Leon-Manna-Pempinelli Equation

2014 ◽  
Vol 912-914 ◽  
pp. 1303-1308 ◽  
Author(s):  
Fu Zhong Lin ◽  
Song Hua Ma
Keyword(s):  
Riccati Equation ◽  
Symbolic Computation ◽  
Expansion Method ◽  
Separation Method ◽  
Variable Separation ◽  
New Family ◽  
Variable Separation Method

In this paper, with the help of symbolic computation system Maple and Riccati equation () expansion method and a linear variable separation method, a new family of variable separation solutions with two arbitrary functions of the (2+1)-dimensional Boiti-Leon-Manna-Pempinelli (BLMP) equation is derived.

Periodic Structures Based on the Symmetrical Lucas Function of the (2+1)-Dimensional Dispersive Long-Wave System

2008 ◽  
Vol 63 (10-11) ◽  
pp. 671-678 ◽  
Author(s):  
Emad A.-B. Abdel-Salam
Keyword(s):  
Riccati Equation ◽  
Periodic Structures ◽  
Main Idea ◽  
Periodic Wave ◽  
Separation Method ◽  
Wave System ◽  
Variable Separation ◽  
Long Wave ◽  
Variable Separation Method

By introducing the Lucas Riccati method and a linear variable separation method, new variable separation solutions with arbitrary functions are derived for a (2+1)-dimensional dispersive longwave system. The main idea of this method is to express the solutions of this system as polynomials in the solution of the Riccati equation that satisfies the symmetrical Lucas functions. From the variable separation solution and by selecting appropriate functions, some novel Jacobian elliptic wave structures and periodic wave evolutional behaviours are investigated.

scholarly journals Load Localization and Reconstruction Using a Variable Separation Method

2019 ◽  
Vol 2019 ◽  
pp. 1-10 ◽  
Author(s):  
Jing Zhang ◽  
Fang Zhang ◽  
Jinhui Jiang
Keyword(s):  
Impulse Response ◽  
Time History ◽  
Separation Method ◽  
Location Information ◽  
Engineering Practice ◽  
Variable Separation ◽  
Response Matrix ◽  
Optimization Function ◽  
Load Location ◽  
Variable Separation Method

Load identification is very important in engineering practice. In this paper, a novel method for load reconstruction and localization is proposed. In the traditional load localization method, location information is coupled to the impulse response matrix. The inversion of the impulse response matrix leads the process of load localization to be time-consuming. So we propose a variable separation method to separate the load location information from the impulse response matrix. An error optimization function of load histories in different modes is employed to determine the true load location. After locating the external load, the load time history can be easily reconstructed by the measurement responses and determinate impulse response matrix. This method is verified by simulations of a simply supported beam acted by a sine load and an impact separately. An experiment is also carried out to validate the feasibility and accuracy of the proposed method.

Painlevé Integrability and Abundant Localized Structures of (2+1)-dimensional Higher Order Broer-Kaup System

2002 ◽  
Vol 57 (12) ◽  
pp. 929-936 ◽  
Author(s):  
Ji Lin ◽  
Hua-mei Li
Keyword(s):  
Phase Shift ◽  
Coherent Structures ◽  
Higher Order ◽  
Separation Method ◽  
Variable Separation ◽  
Localized Structures ◽  
Painlevé Property ◽  
Variable Separation Method ◽  
Truncated Painlevé Expansion

It is proven that the (2+1) dimensional higher-order Broer-Kaup system the possesses the Painlevé property, using the Weiss-Tabor-Carnevale method and Kruskal’s simplification. Abundant localized coherent structures are obtained by using the standard truncated Painlevé expansion and the variable separation method. Fractal dromion solutions and multi-peakon structures are discussed. The interactions of three peakons are investigated. The interactions among the peakons are not elastic; they interchange their shapes but there is no phase shift

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