scholarly journals Exact solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation via the first integral method

2012 ◽  
Vol 17 (4) ◽  
pp. 481-488 ◽  
Author(s):  
Mohammad Mirzazadeh ◽  
Mostafa Eslami
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Telegraph Equation ◽  
First Integral Method ◽  
Wave Solutions ◽  
Nonlinear Telegraph Equation

In this article we find the exact traveling wave solutions of the Kudryashov–Sinelshchikov equation and nonlinear telegraph equation by using the first integral method. This method is based on the theory of commutative algebra. This method can be applied to nonintegrable equations as well as to integrable ones.

scholarly journals The first integral method and traveling wave solutions to Davey–Stewartson equation

2012 ◽  
Vol 17 (2) ◽  
pp. 182-193 ◽  
Author(s):  
Hossein Jafari ◽  
Atefe Sooraki ◽  
Yahya Talebi ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Soliton Solution ◽  
Commutative Algebra ◽  
Traveling Wave ◽  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
First Integral Method ◽  
Wave Solutions

In this paper, the first integral method will be applied to integrate the Davey–Stewartson’s equation. Using this method, a few exact solutions will be obtained using ideas from the theory of commutative algebra. Finally, soliton solution will also be obtained using the traveling wave hypothesis.

scholarly journals Travelling Wave Solutions to the Generalized Pochhammer-Chree (PC) Equations Using the First Integral Method

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Shoukry Ibrahim Atia El-Ganaini
Keyword(s):  
Integral Method ◽  
Traveling Wave Solutions ◽  
First Integral ◽  
Periodic Wave ◽  
Travelling Wave ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions ◽  
Manageable Method ◽  
Complex Exponential

By using the first integral method, the traveling wave solutions for the generalized Pochhammer-Chree (PC) equations are constructed. The obtained results include complex exponential function solutions, complex traveling solitary wave solutions, complex periodic wave solutions, and complex rational function solutions. The power of this manageable method is confirmed.

scholarly journals The First-Integral Method and Abundant Explicit Exact Solutions to the Zakharov Equations

2012 ◽  
Vol 2012 ◽  
pp. 1-16 ◽  
Author(s):  
Yadong Shang ◽  
Xiaoxiao Zheng
Keyword(s):  
Solitary Wave ◽  
Exact Solutions ◽  
Elliptic Function ◽  
Integral Method ◽  
First Integral ◽  
Periodic Wave ◽  
Solitary Wave Solutions ◽  
First Integral Method ◽  
Periodic Wave Solutions ◽  
Wave Solutions

This paper is concerned with the system of Zakharov equations which involves the interactions between Langmuir and ion-acoustic waves in plasma. Abundant explicit and exact solutions of the system of Zakharov equations are derived uniformly by using the first integral method. These exact solutions are include that of the solitary wave solutions of bell-type fornandE, the solitary wave solutions of kink-type forEand bell-type forn, the singular traveling wave solutions, periodic wave solutions of triangle functions, Jacobi elliptic function doubly periodic solutions, and Weierstrass elliptic function doubly periodic wave solutions. The results obtained confirm that the first integral method is an efficient technique for analytic treatment of a wide variety of nonlinear systems of partial differential equations.

Exact solutions for the fractional differential equations by using the first integral method

2015 ◽  
Vol 4 (1) ◽  
Author(s):  
Hossein Aminikhah ◽  
A. Refahi Sheikhani ◽  
Hadi Rezazadeh
Keyword(s):  
Differential Equations ◽  
Exact Solutions ◽  
Fractional Differential Equations ◽  
Commutative Algebra ◽  
Integral Method ◽  
First Integral ◽  
Ring Theory ◽  
First Integral Method ◽  
Fractional Differential ◽  
Method Show

AbstractIn this paper, we apply the first integral method to study the solutions of the nonlinear fractional modified Benjamin-Bona-Mahony equation, the nonlinear fractional modified Zakharov-Kuznetsov equation and the nonlinear fractional Whitham-Broer-Kaup-Like systems. This method is based on the ring theory of commutative algebra. The results obtained by the proposed method show that the approach is effective and general. This approach can also be applied to other nonlinear fractional differential equations, which are arising in the theory of solitons and other areas.

scholarly journals Solutions of Kudryashov - Sinelshchikov equation and generalized Radhakrishnan-Kundu-Lakshmanan equation by the first integral method

2016 ◽  
Vol 4 (2) ◽  
pp. 37 ◽  
Author(s):  
Salam Subhaschandra Singh
Keyword(s):  
Exact Solutions ◽  
Commutative Algebra ◽  
Integral Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Nonlinear Partial Differential Equations ◽  
Algebraic Method ◽  
First Integral ◽  
Nonlinear Evolution Equations ◽  
First Integral Method

This paper shows the applicability of the First Integral Method in obtaining solutions of Nonlinear Partial Differential Equations (NLPDEs). The method is applied in constructing solutions of Kudryashov-Sinelshchikov equation (KSE) and Generalized Radhakrishnan-Kundu-Lakshmanan Equation (GRKLE). The First Integral Method, which is based on the Ring Theory of Commutative Algebra, is a direct algebraic method for obtaining exact solutions of NLPDEs. This method is applicable to integrable as well as nonintegrable NLPDEs. The method is an efficient method for obtaining exact solutions of many Nonlinear Evolution Equations (NLEEs).

scholarly journals Five semi analytical and numerical simulations for the fractional nonlinear space-time telegraph equation

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Mostafa M. A. Khater ◽  
Choonkil Park ◽  
Jung Rye Lee ◽  
Mohamed S. Mohamed ◽  
Raghda A. M. Attia
Keyword(s):  
Numerical Simulations ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Approximate Solutions ◽  
Telegraph Equation ◽  
Space Time ◽  
Numerical Techniques ◽  
B Spline ◽  
Wave Solutions ◽  
Adomian Decomposition

AbstractThe accuracy of analytical obtained solutions of the fractional nonlinear space–time telegraph equation that has been constructed in (Hamed and Khater in J. Math., 2020) is checked through five recent semi-analytical and numerical techniques. Adomian decomposition (AD), El Kalla (EK), cubic B-spline (CBS), extended cubic B-spline (ECBS), and exponential cubic B-spline (ExCBS) schemes are used to explain the matching between analytical and approximate solutions, which shows the accuracy of constructed traveling wave solutions. In 1880, Oliver Heaviside derived the considered model to describe the cutting-edge or voltage of an electrified transmission. The matching between solutions has been explained by plotting them in some different sketches.

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