New exact solutions of nonlinear conformable time-fractional Boussinesq equations using the modified Kudryashov method

2017 ◽  
Vol 27 (4) ◽  
pp. 628-636 ◽  
Author(s):  
K. Hosseini ◽  
R. Ansari
Keyword(s):  
Exact Solutions ◽  
Boussinesq Equations ◽  
New Exact Solutions ◽  
Modified Kudryashov Method ◽  
Kudryashov Method

scholarly journals New exact solutions of the combined and double combined sinh-cosh-Gordon equations via modified Kudryashov method

2018 ◽  
Vol 6 (1) ◽  
pp. 25 ◽  
Author(s):  
Atish Kumar Joardar ◽  
Dipankar Kumar ◽  
K. M. Abdul Al Woadud
Keyword(s):  
Exact Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Actual Behavior ◽  
New Exact Solutions ◽  
Modified Kudryashov Method ◽  
Painlevé Property ◽  
Wide Range ◽  
Kudryashov Method ◽  
Package Program ◽  
Maple Package

The combined and double combined sinh-cosh-Gordon equations are very important to a wide range of various scientific applications that ranges from chemical reactions to water surface gravity waves. In this article, with the assistance of a function transform and Painlevè property, the nonlinear combined and double combined sinh-cosh-Gordon equations turn into ordinary differential equations. Later on, modified Kudryashov method is adopted for investigating new analytical solution of the studied equations. As a consequence, a series of new analytical solutions are acquired and we demonstrated the actual behavior of the achieved solutions of the mentioned equations with the aid of 3D and 2D MATLAB graphs. Finally, we also validate the effectiveness of the modified Kudryashov method for the problem of extracting new exact solutions of the combined and double combined sinh-cosh-Gordon equations with the aid of Maple package program. It is shown that the implemented method is capable to extract new solutions and it can also use to other nonlinear partial differential equation (NLPDE's) arising in mathematical physics or other applied field.

scholarly journals Modified Kudryashov Method to Solve Generalized Kuramoto-Sivashinsky Equation

Symmetry ◽  
2018 ◽  
Vol 10 (10) ◽  
pp. 527 ◽  
Author(s):  
Adem Kilicman ◽  
Rathinavel Silambarasan
Keyword(s):  
Differential Equation ◽  
Exact Solutions ◽  
Nonlinear Partial Differential Equation ◽  
Complex Structures ◽  
Algebraic Equations ◽  
New Exact Solutions ◽  
Modified Kudryashov Method ◽  
Kudryashov Method ◽  
The Given ◽  
Sivashinsky Equation

The generalized Kuramoto–Sivashinsky equation is investigated using the modified Kudryashov method for the new exact solutions. The modified Kudryashov method converts the given nonlinear partial differential equation to algebraic equations, as a result of various steps, which upon solving the so-obtained equation systems yields the analytical solution. By this way, various exact solutions including complex structures are found, and their behavior is drawn in the 2D plane by Maple to compare the uniqueness and wave traveling of the solutions.

scholarly journals On the Variant Boussinesq Equations

1997 ◽  
Vol 52 (4) ◽  
pp. 335-336
Author(s):  
Yi-Tian Gao ◽  
Bo Tian
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Boussinesq Equations ◽  
New Exact Solutions ◽  
Variant Boussinesq Equations

Abstract We extend the generalized tan h method to the variant Boussinesq equations and obtain certain solitary-wave and new exact solutions.

New exact solutions for nonlinear Atangana conformable Boussinesq-like equations by new Kudryashov method

2021 ◽  
pp. 2150163
Author(s):  
Seyed Mehdi Mirhosseini-Alizamini ◽  
Najib Ullah ◽  
Jamilu Sabi’u ◽  
Hadi Rezazadeh ◽  
Mustafa Inc
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Physical Phenomenon ◽  
Ocean Engineering ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Different Types

In this work, we investigate a new Kudryashov method (NKM) to find the exact and some new solutions of four different types of nonlinear Atangana conformable Boussinesq-like equations (NLACBEs). This is an appropriate algorithm for finding the exact solutions and also working for different types of nonlinear confirmable differential equations. In coastal and ocean engineering, some physical phenomenon is based on the exact solutions of the NLACBEs.

New exact solutions for the Wick-type stochastic Zakharov–Kuznetsov equation for modelling waves on shallow water surfaces

2017 ◽  
Vol 25 (2) ◽  
Author(s):  
S. Saha Ray ◽  
S. Singh
Keyword(s):  
Differential Equation ◽  
Partial Differential Equation ◽  
Exact Solution ◽  
Exact Solutions ◽  
White Noise ◽  
Shallow Water ◽  
Hermite Transform ◽  
New Exact Solutions ◽  
Kudryashov Method ◽  
Stochastic Solution

AbstractIn this article, an exact solution of the Wick-type stochastic Zakharov–Kuznetsov equation has been obtained by using the Kudryashov method. We have used the Hermite transform for transforming the Wick-type stochastic Zakharov–Kuznetsov equation into a deterministic partial differential equation. Also we have applied the inverse Hermite transform for obtaining a set of stochastic solution in the white noise space.

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