scholarly journals A general sub-equation method to the burgers-like equation

2017 ◽  
Vol 21 (4) ◽  
pp. 1681-1687 ◽  
Author(s):  
Xiao-Min Wang ◽  
Su-Dao Bilige ◽  
Yue-Xing Bai
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Rational Solutions ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Potential Applications

A Burgers-like equation is studied by a general sub-equation method, and some new exact solutions are obtained, which include the traveling wave solutions, non-traveling wave solutions, multi-soliton solutions, rational solutions, and other types of solutions. The obtained results are important in thermal science, and potential applications can be found.

Abundant soliton solutions for the Hirota–Maccari equation via the generalized exponential rational function method

2019 ◽  
Vol 33 (09) ◽  
pp. 1950106 ◽  
Author(s):  
Behzad Ghanbari
Keyword(s):  
Exact Solutions ◽  
Rational Function ◽  
Traveling Wave ◽  
Function Method ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Graphical Interpretation ◽  
Wave Solutions ◽  
Complex Models ◽  
Exponential Rational Function Method

In this paper, some new traveling wave solutions to the Hirota–Maccari equation are constructed with the help of the newly introduced method called generalized exponential rational function method. Several families of exact solutions are found corresponding to the equation. To the best of our knowledge, these solutions are new, and have never been addressed in the literature. The graphical interpretation of the solutions is also depicted. Moreover, it is contemplated that the proposed technique can also be employed to another sort of complex models.

scholarly journals Exact Traveling Wave Solutions of Certain Nonlinear Partial Differential Equations Using the G′/G2-Expansion Method

2018 ◽  
Vol 2018 ◽  
pp. 1-15 ◽  
Author(s):  
Sekson Sirisubtawee ◽  
Sanoe Koonprasert
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Exact Solutions ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Traveling Wave Solutions ◽  
Expansion Method ◽  
Rational Solutions ◽  
Partial Differential ◽  
Wave Solutions

We apply the G′/G2-expansion method to construct exact solutions of three interesting problems in physics and nanobiosciences which are modeled by nonlinear partial differential equations (NPDEs). The problems to which we want to obtain exact solutions consist of the Benny-Luke equation, the equation of nanoionic currents along microtubules, and the generalized Hirota-Satsuma coupled KdV system. The obtained exact solutions of the problems via using the method are categorized into three types including trigonometric solutions, exponential solutions, and rational solutions. The applications of the method are simple, efficient, and reliable by means of using a symbolically computational package. Applying the proposed method to the problems, we have some innovative exact solutions which are different from the ones obtained using other methods employed previously.

New exact traveling wave solutions of biological population model via the extended rational sinh-cosh method and the modified Khater method

2019 ◽  
Vol 33 (28) ◽  
pp. 1950338 ◽  
Author(s):  
Hadi Rezazadeh ◽  
Alper Korkmaz ◽  
Mostafa M. A. Khater ◽  
Mostafa Eslami ◽  
Dianchen Lu ◽  
...  
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Population Model ◽  
Stability Property ◽  
Traveling Wave Solutions ◽  
Algebraic Methods ◽  
New Exact Solutions ◽  
Wave Solutions ◽  
Biological Population ◽  
The Stability

In this paper, the extended rational sinh-cosh method (ERSCM) and modified Khater method are applied to the biological population model to derive new exact solutions. Moreover, the stability property of some obtained solutions is discussed to show the ability of them for using in the model’s applications. Implementation of the direct algebraic methods, the equations derived by substitution of the predicted solution are solved. It is significant to point out that new traveling wave solutions are found. The present methods are easy to employ and sufficient to determine the solutions.

New traveling wave solutions of the perturbed nonlinear Schrödingers equation in the left-handed metamaterials

2018 ◽  
Vol 13 (01) ◽  
pp. 2050022 ◽  
Author(s):  
Alphonse Houwe ◽  
Mibaile Justin ◽  
Serge Y. Doka ◽  
Kofane Timoleon Crepin
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Fiber Optic ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Simple Equation ◽  
Left Handed ◽  
Wave Solutions ◽  
Generalized Kudryashov Method ◽  
Kudryashov Method

This paper extracts the analytical soliton solutions of the perturbed NLSE given in (1). We use successfully two integration methods namely the extended simple equation method and generalized Kudryashov method. In view of the results obtained, some new additional ones have been obtained. The results are dark, bright and exact solutions that propagate in the fiber optic and left-handed metamaterials (LHMs).

Symbolic computations: Dispersive soliton solutions for (3+1)-dimensional Boussinesq and Kadomtsev–Petviashvili dynamical equations and its applications

2019 ◽  
Vol 33 (29) ◽  
pp. 1950342 ◽  
Author(s):  
Aly R. Seadawy ◽  
Kalim U. Tariq ◽  
Jian-Guo Liu
Keyword(s):  
Partial Differential Equations ◽  
Differential Equations ◽  
Traveling Wave ◽  
Nonlinear Partial Differential Equations ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Equation Method ◽  
Dynamical Equations ◽  
Wave Solutions ◽  
Kp Equations

In this paper, the auxiliary expansion equation method is applied to compute the analytical wave solutions for (3[Formula: see text]+[Formula: see text]1)-dimensional Boussinesq and Kadomtsev–Petviashvili (KP) equations. A simple transformation is carried out to reduce the set of nonlinear partial differential equations (NPDEs) into ODEs. These obtained results hold numerous traveling wave solutions that are of key importance in elucidating some physical circumstance.

scholarly journals On the exact solutions of the fractional (2+1)- dimensional Davey - Stewartson equation system

2017 ◽  
Vol 7 (3) ◽  
pp. 265-270
Author(s):  
Gülnur Yel ◽  
Zeynep Fidan Koçak
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Traveling Wave Solutions ◽  
Equation System ◽  
Trigonometric Function ◽  
Equation Method ◽  
Exact Traveling Wave Solutions ◽  
Trial Equation Method ◽  
Wave Solutions ◽  
Trigonometric Function Solutions

In this work, we construct the exact traveling wave solutions of the fractional (2+1)-dimensional Davey-Stewartson equation system (D-S) that is complex equation system using the Modified Trial Equation Method (MTEM). We obtained trigonometric function solutions by this method that are new in literature.

scholarly journals Exact Solutions to KdV6 Equation by Using a New Approach of the Projective Riccati Equation Method

2010 ◽  
Vol 2010 ◽  
pp. 1-10 ◽  
Author(s):  
Cesar A. Gómez S ◽  
Alvaro H. Salas ◽  
Bernardo Acevedo Frias
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Point Of View ◽  
Computational Method ◽  
New Approach ◽  
Wave Solutions ◽  
Projective Riccati Equation Method ◽  
Kdv6 Equation

We study a new integrable KdV6 equation from the point of view of its exact solutions by using an improved computational method. A new approach to the projective Riccati equations method is implemented and used to construct traveling wave solutions for a new integrable system, which is equivalent to KdV6 equation. Periodic and soliton solutions are formally derived. Finally, some conclusions are given.

scholarly journals Exact Traveling Wave Solutions of Explicit Type, Implicit Type, and Parametric Type forK(m,n)Equation

2012 ◽  
Vol 2012 ◽  
pp. 1-23 ◽  
Author(s):  
Xianbin Wu ◽  
Weiguo Rui ◽  
Xiaochun Hong
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Soliton Solutions ◽  
Traveling Wave Solutions ◽  
Periodic Wave ◽  
Bifurcation Method ◽  
Periodic Wave Solutions ◽  
Exact Traveling Wave Solutions ◽  
Wave Solutions

By using the integral bifurcation method, we study the nonlinearK(m,n)equation for all possible values ofmandn. Some new exact traveling wave solutions of explicit type, implicit type, and parametric type are obtained. These exact solutions include peculiar compacton solutions, singular periodic wave solutions, compacton-like periodic wave solutions, periodic blowup solutions, smooth soliton solutions, and kink and antikink wave solutions. The great parts of them are different from the results in existing references. In order to show their dynamic profiles intuitively, the solutions ofK(n,n),K(2n−1,n),K(3n−2,n),K(4n−3,n), andK(m,1)equations are chosen to illustrate with the concrete features.

scholarly journals New exact traveling wave solutions for DS-I and DS-II equations

2012 ◽  
Vol 17 (3) ◽  
pp. 369-378 ◽  
Author(s):  
Ahmet Yildirim ◽  
Ameneh Samiei Paghaleh ◽  
Mohammad Mirzazadeh ◽  
Hossein Moosaei ◽  
Anjan Biswas
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Solution Method ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Equation Method ◽  
Wave Solutions ◽  
Simplest Equation Method

In this present work, the simplest equation method is used to construct exact solutions of the DS-I and DS-II equations. The simplest equation method is a powerful solution method for obtaining exact solutions of nonlinear evolution equations. This method can be applied to nonintegrable equations as well as to integrable ones.

scholarly journals Some New Traveling Wave Exact Solutions of the (2+1)-Dimensional Boiti-Leon-Pempinelli Equations

2014 ◽  
Vol 2014 ◽  
pp. 1-9 ◽  
Author(s):  
Jian-ming Qi ◽  
Fu Zhang ◽  
Wen-jun Yuan ◽  
Zi-feng Huang
Keyword(s):  
Exact Solutions ◽  
Traveling Wave ◽  
Evolution Equations ◽  
Nonlinear Evolution ◽  
Traveling Wave Solutions ◽  
Nonlinear Evolution Equations ◽  
Complex Method ◽  
Rational Solutions ◽  
Wave Solutions ◽  
Periodic Traveling Wave

We employ the complex method to obtain all meromorphic exact solutions of complex (2+1)-dimensional Boiti-Leon-Pempinelli equations (BLP system of equations). The idea introduced in this paper can be applied to other nonlinear evolution equations. Our results show that all rational and simply periodic traveling wave exact solutions of the equations (BLP) are solitary wave solutions, the complex method is simpler than other methods, and there exist some rational solutionsur,2(z)and simply periodic solutionsus,2–6(z)which are not only new but also not degenerated successively by the elliptic function solutions. We believe that this method should play an important role for finding exact solutions in the mathematical physics. For these new traveling wave solutions, we give some computer simulations to illustrate our main results.

Sign in / Sign up

Export Citation Format

Share Document