MULTIPLE EXACT SOLUTIONS OF THE GENERALIZED TIME FRACTIONAL FOAM DRAINAGE EQUATION

Fractals ◽  
2020 ◽  
Vol 28 (04) ◽  
pp. 2050062
Author(s):  
DANDAN SHI ◽  
YUFENG ZHANG ◽  
WENHAO LIU
Keyword(s):  
Exact Solutions ◽  
Expansion Method ◽  
Transformation Method ◽  
Vertical Density Profile ◽  
New Exact Solutions ◽  
Vertical Density ◽  
Foam Drainage Equation ◽  
Physical Phenomena ◽  
Generalized Time ◽  
Foam Drainage

In this paper, we investigate the exact solutions of the generalized time fractional foam drainage equation. The Lie-group scaling transformation method and improved [Formula: see text]-expansion method are adopted here. The equation describes the evolution of the vertical density profile of a foam under gravity. New exact solutions and maple diagrams of the generalized time fractional foam drainage equation can help us better understand the physical phenomena.

AUTO-BÄCKLUND TRANSFORMATION AND NEW EXACT SOLUTIONS OF THE (2 + 1)-DIMENSIONAL NIZHNIK–NOVIKOV–VESELOV EQUATION

2005 ◽  
Vol 16 (03) ◽  
pp. 393-412 ◽  
Author(s):  
DENGSHAN WANG ◽  
HONG-QING ZHANG
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Bäcklund Transformation ◽  
Rational Solution ◽  
Expansion Method ◽  
Backlund Transformation ◽  
Paper Making ◽  
New Exact Solutions ◽  
Physical Phenomena ◽  
Series Expansion Method

In this paper, making use of the truncated Laurent series expansion method and symbolic computation we get the auto-Bäcklund transformation of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation. As a result, single soliton solution, single soliton-like solution, multi-soliton solution, multi-soliton-like solution, the rational solution and other exact solutions of the (2 + 1)-dimensional Nizhnik–Novikov–Veselov equation are found. These solutions may be useful to explain some physical phenomena.

A Class of Exact Solutions of (3+1)-Dimensional Generalized B-Type Kadomtsev–Petviashvili Equation

2017 ◽  
Vol 18 (2) ◽  
pp. 137-143 ◽  
Author(s):  
Shuang Liu ◽  
Yao Ding ◽  
Jian-Guo Liu
Keyword(s):  
Exact Solutions ◽  
Symbolic Computation ◽  
Traveling Wave ◽  
Expansion Method ◽  
Trigonometric Function ◽  
Hyperbolic Function ◽  
New Exact Solutions ◽  
Petviashvili Equation

AbstractBy employing the generalized$(G'/G)$-expansion method and symbolic computation, we obtain new exact solutions of the (3 + 1) dimensional generalized B-type Kadomtsev–Petviashvili equation, which include the traveling wave exact solutions and the non-traveling wave exact solutions showed by the hyperbolic function and the trigonometric function. Meanwhile, some interesting physics structure are discussed.

scholarly journals Travelling Wave Solutions of the Perturbed Wadati-Segur-Ablowitz Equation by (G'/G)-Expansion Method

2018 ◽  
Vol 6 (06) ◽  
Author(s):  
Figen Kangalgil
Keyword(s):  
Exact Solutions ◽  
Rational Functions ◽  
Expansion Method ◽  
Mathematical Physics ◽  
Travelling Wave ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Nonlinear Physical Phenomena ◽  
Physical Phenomena

The investigation of the exact solutions of NLPDEs plays an im- portant role for the understanding of most nonlinear physical phenomena. Also, the exact solutions of this equations aid the numerical solvers to assess the correctness of their results. In this paper, (G'/G)-expansion method is pre- sented to construct exact solutions of the Perturbed Wadati-Segur-Ablowitz equation. Obtained the exact solutions are expressed by the hyperbolic, the trigonometric and the rational functions. All calculations have been made with the aid of Maple program. It is shown that the proposed algorithm is elemen- tary, e¤ective and has been used for many PDEs in mathematical physics.  

Exact solutions for nonlinear foam drainage equation

2016 ◽  
Vol 91 (2) ◽  
pp. 209-218 ◽  
Author(s):  
E. M. E. Zayed ◽  
Abdul-Ghani Al-Nowehy
Keyword(s):  
Exact Solutions ◽  
Foam Drainage Equation ◽  
Foam Drainage

Explicit solutions to nonlinear Chen–Lee–Liu equation

2021 ◽  
pp. 2150438
Author(s):  
Lanre Akinyemi ◽  
Najib Ullah ◽  
Yasir Akbar ◽  
Mir Sajjad Hashemi ◽  
Arzu Akbulut ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Nonlinear Partial Differential Equations ◽  
Elliptic Functions ◽  
Expansion Method ◽  
Nonlinear Phenomena ◽  
Explicit Solutions ◽  
Mathematical Algorithm ◽  
New Exact Solutions ◽  
Order Polynomial ◽  
Fourth Order Polynomial

In this work, a generalized [Formula: see text]-expansion method has been used for solving the nonlinear Chen–Lee–Liu equation. This method is a more common, general, and powerful mathematical algorithm for finding the exact solutions of nonlinear partial differential equations (NPDEs), where [Formula: see text] follows the Jacobi elliptic equation [Formula: see text], and we let [Formula: see text] be a fourth-order polynomial. Many new exact solutions such as the hyperbolic, rational, and trigonometric solutions with different parameters in terms of the Jacobi elliptic functions are obtained. The distinct solutions obtained in this paper clearly explain the importance of some physical structures in the field of nonlinear phenomena. Also, this method deals very well with higher-order nonlinear equations in the field of science. The numerical results described in the plots were obtained by using Maple.

Solitary dynamics of longitudinal wave equation arises in magneto-electro-elastic circular rod

2020 ◽  
pp. 2150086 ◽  
Author(s):  
Naila Sajid ◽  
Ghazala Akram
Keyword(s):  
Wave Equation ◽  
Exact Solutions ◽  
Longitudinal Wave ◽  
Mapping Method ◽  
Integration Scheme ◽  
Auxiliary Equation ◽  
New Exact Solutions ◽  
Non Linear ◽  
Physical Phenomena

This paper examines the effectiveness of an integration scheme, which called the extended modified auxiliary equation mapping method in exactly solving a well-known non-linear longitudinal wave equation with dispersion caused by transverse Poisson’s effect arises in a magneto-electro-elastic (MEE) circular rod. Explicit new exact solutions are derived in different form such as hyperbolic, kinky, anti-kinky, dark, and singular solitons of the longitudinal wave equation. The movements of obtained solutions are shown graphically, which helps to understand the physical phenomena.

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