scholarly journals KAJIAN TENTANG METODE PERSAMAAN RICCATI PROYEKTIF

2018 ◽  
Vol 7 (2) ◽  
pp. 53
Author(s):  
Fitri Yessi Jami
Keyword(s):  
Riccati Equation ◽  
Equation Method ◽  
Balance Principle ◽  
Projective Riccati Equation Method

Abstract. In this paper, we discuss the derivation and application of a projective Riccatiequation method in solving nonlinear partial dierential equations. We also study themathematical aspects of the method and its limitations in some particular cases.Kata Kunci: Nonlinear partial dierential equations, projective Riccati equation method,dominant balance principle

NEW TYPES OF INTERACTIONS BASED ON VARIABLE SEPARATION SOLUTIONS VIA THE GENERAL PROJECTIVE RICCATI EQUATION METHOD

2007 ◽  
Vol 19 (02) ◽  
pp. 195-226 ◽  
Author(s):  
CHAO-QING DAI ◽  
JIE-FANG ZHANG
Keyword(s):  
Riccati Equation ◽  
Equation Method ◽  
Wave System ◽  
Variable Separation ◽  
The Common ◽  
Novel Interactions ◽  
Dimensional Models ◽  
The One ◽  
Multivalued Functions ◽  
Projective Riccati Equation Method

In this paper, first, the general projective Riccati equation method (PREM) is applied to derive variable separation solutions of (2 + 1)-dimensional systems. By further studying, we find that these variable separation solutions obtained by PREM, which seem independent, actually depend on each other. A common formula with some arbitrary functions is obtained to describe suitable physical quantities for some (2 + 1)-dimensional models such as the generalized Nizhnik–Novikov–Veselov system, Broer–Kaup–Kupershmidt equation, dispersive long wave system, Boiti–Leon–Pempinelli model, generalized Burgers model, generalized Ablowitz–Kaup–Newell–Segur system and Maccari equation. The universal formula in Tang, Lou, and Zhang [2] can be simplified to the common formula in the present paper. Second, this method is successfully generalized to (1 + 1)-dimensional systems, such as coupled integrable dispersionless equations, shallow water wave equation, Boiti system and negative KdV model, and is able to obtain another common formula to describe suitable physical fields or potentials of these (1 + 1)-dimensional models, which is similar to the one in (2 + 1)-dimensional systems. Finally, based on the common formula for (2 + 1)-dimensional systems and by selecting appropriate multivalued functions, elastic and inelastic interactions among special dromion, special peakon, foldon and semi-foldon are investigated. Furthermore, the explicit phase shifts for all the local excitations offered by the common formula have been given, and are applied to these novel interactions in detail.

scholarly journals A modified generalized projective Riccati equation method

2016 ◽  
Vol 12 (6) ◽  
pp. 6318-6334
Author(s):  
Luwai Wazzan ◽  
Shafeek A Ghaleb
Keyword(s):  
Exact Solutions ◽  
Riccati Equation ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
New Exact Solutions ◽  
Special Cases ◽  
Projective Riccati Equation Method

A modification of the generalized projective Riccati equation method is proposed to treat some nonlinear evolution equations and obtain their exact solutions. Some known methods are obtained as special cases of the proposed method. In addition, the method is implemented to find new exact solutions for the well-known Dreinfelds-Sokolov-Wilson system of nonlinear partial differential equations.

Solitons with Fusion and Fission Properties in the (2+1)-Dimensional Modified Dispersive Water-Wave System

2006 ◽  
Vol 61 (7-8) ◽  
pp. 307-315 ◽  
Author(s):  
Chao-Qing Dai ◽  
Rui-Pin Chen
Keyword(s):  
Riccati Equation ◽  
Water Wave ◽  
Equation Method ◽  
Wave System ◽  
Variable Separation ◽  
Projective Riccati Equation Method

In this paper, by means of the general projective Riccati equation method (PREM), the variable separation solutions of the (2+1)-dimensional modified dispersive water-wave system are obtained. By further studying, we find that these variable separation solutions, which seem independent, actually depend on each other. Based on the special variable separation solution and choosing suitable functions p and q, soliton fusion and fission phenomena among peakons, compactons, dromions and semifoldons are firstly investigated. - PACS numbers: 05.45.Yv, 02.30.Jr, 02.03Ik

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