Solitary wave solutions of selective nonlinear diffusion-reaction equations using homogeneous balance method

Pramana ◽  
2010 ◽  
Vol 75 (4) ◽  
pp. 607-616 ◽  
Author(s):  
Ranjit Kumar ◽  
R. S. Kaushal ◽  
Awadhesh Prasad
Keyword(s):  
Solitary Wave ◽  
Nonlinear Diffusion ◽  
Balance Method ◽  
Diffusion Reaction ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
Homogeneous Balance Method ◽  
Reaction Equations ◽  
Homogeneous Balance

NEW TYPES OF MULTIPLE SOLITARY WAVE SOLUTIONS FOR THE HIGH-ORDER BROER–KAUP EQUATIONS

2009 ◽  
Vol 23 (09) ◽  
pp. 2261-2267 ◽  
Author(s):  
CHENG-JIE BAI ◽  
HONG ZHAO ◽  
XIA ZHANG ◽  
HENG-YING XU
Keyword(s):  
Solitary Wave ◽  
Nonlinear Equation ◽  
High Order ◽  
Balance Method ◽  
Solitary Wave Solutions ◽  
Wave Solutions ◽  
New Type ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

Using the extended homogeneous balance method, we obtain a new type of multiple solitary wave solutions for the (1+1)-dimensional high-order Broer–Kaup equations and a new type of multiple solitary wave-like solutions for the (2+1)-dimensional high-order BK equations. The method used here is very concise and primary, and can be generalized to deal with other class of nonlinear equation.

The nonlinear diffusion reaction dynamical system with quadratic and cubic nonlinearities with analytical investigations

2020 ◽  
Vol 34 (09) ◽  
pp. 2050085 ◽  
Author(s):  
Aly R. Seadawy ◽  
Mujahid Iqbal ◽  
Dianchen Lu
Keyword(s):  
Solitary Wave ◽  
Nonlinear Diffusion ◽  
Research Work ◽  
Periodic Wave ◽  
Diffusion Reaction ◽  
New Technique ◽  
Solitary Wave Solutions ◽  
Bright Solitons ◽  
Wave Solutions ◽  
Quadratic And Cubic Nonlinearities

Our aim in this research work is to formulate the exact traveling and solitary wave solutions of nonlinear diffusion reaction (DR) equation with quadratic and cubic nonlinearities by implementing the new technique which is a modified mathematical method. We have investigated the density independent nonlinear diffusion equation with convective flux term. As a result, we have found a variety of new exact traveling and solitary wave solutions in the form of dark solitons, bright solitons, combined dark-bright solitons, traveling wave, periodic wave solutions and we also represent the physical structure of the obtained solutions by two- and three-dimensional graphics by using the Mathematica software. This work proves the power, reliability and fruitfulness of this new technique.

scholarly journals New fractional calculus and application to the fractional-order of extended biological population model

2018 ◽  
Vol 36 (3) ◽  
pp. 115-128 ◽  
Author(s):  
Ahmad Neirameh
Keyword(s):  
Solitary Wave ◽  
Fractional Order ◽  
Population Model ◽  
Conformable Fractional Derivative ◽  
Solitary Wave Solutions ◽  
Fractional Partial Differential Equations ◽  
Wave Solutions ◽  
Biological Population ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this study, we propose a new algorithm to find exact solitary wave solutions of nonlinear time- fractional order of extended biological population model. The new algorithm basically illustrates how two powerful algorithms, conformable fractional derivative and the homogeneous balance method can be combined and used to get exact solutions of fractional partial differential equations.

Solitary and Travelling Wave Solutions of Certain Nonlinear Diffusion-Reaction Equations

2020 ◽  
Author(s):  
Miftachul Hadi
Keyword(s):  
Nonlinear Diffusion ◽  
Travelling Wave ◽  
Diffusion Reaction ◽  
Travelling Wave Solutions ◽  
Wave Solutions ◽  
Reaction Equations

We review the work of Ranjit Kumar, R S Kaushal, Awadhesh Prasad. The work is still in progress.

scholarly journals Analytical Wave Solutions for Foam and KdV-Burgers Equations Using Extended Homogeneous Balance Method

Mathematics ◽  
2019 ◽  
Vol 7 (8) ◽  
pp. 729 ◽  
Author(s):  
U.M. Abdelsalam ◽  
M. G. M. Ghazal
Keyword(s):  
Evolution Equations ◽  
Traveling Wave Solutions ◽  
Industrial Applications ◽  
Nonlinear Evolution Equations ◽  
Balance Method ◽  
Wave Solutions ◽  
Engineering Sciences ◽  
Foam Drainage Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this paper, extended homogeneous balance method is presented with the aid of computer algebraic system Mathematica for deriving new exact traveling wave solutions for the foam drainage equation and the Kowerteg-de Vries–Burgers equation which have many applications in industrial applications and plasma physics. The method is effective to construct a series of analytical solutions including many types like periodical, rational, singular, shock, and soliton wave solutions for a wide class of nonlinear evolution equations in mathematical physics and engineering sciences.

scholarly journals Travelling Wave Solutions for Fisher’s Equation Using the Extended Homogeneous Balance Method

2021 ◽  
Vol 26 (1) ◽  
pp. 22-30
Author(s):  
Mohammad M. Fares ◽  
Usama M. Abdelsalam ◽  
Faiza M. Allehiany
Keyword(s):  
Travelling Wave ◽  
Nonlinear Evolution Equations ◽  
Balance Method ◽  
Fisher Equation ◽  
Travelling Wave Solutions ◽  
Fisher’S Equation ◽  
Wave Solutions ◽  
Fisher's Equation ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance

In this work, the extended homogeneous balance method is used to derive exact solutions of nonlinear evolution equations. With the aid of symbolic computation, many new exact travelling wave solutions have been obtained for Fisher’s equation and Burgers-Fisher equation. Fisher’s equation has been widely used in studying the population for various systems, especially in biology, while Burgers-Fisher equation has many physical applications such as in gas dynamics and fluid mechanics. The method used can be applied to obtain multiple travelling wave solutions for nonlinear partial differential equations.

scholarly journals Analytical solution of Balitsky-Kovchegov equation with homogeneous balance method

2021 ◽  
Vol 103 (5) ◽  
Author(s):  
Xiaopeng Wang ◽  
Yirui Yang ◽  
Wei Kou ◽  
Rong Wang ◽  
Xurong Chen
Keyword(s):  
Analytical Solution ◽  
Balance Method ◽  
Homogeneous Balance Method ◽  
Homogeneous Balance
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