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New Exact Solutions of Fractional Zakharov–Kuznetsov and Modified Zakharov–Kuznetsov Equations Using Fractional Sub-Equation Method 被引量:3
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作者 S.Saha Ray S.Sahoo 《Communications in Theoretical Physics》 SCIE CAS CSCD 2015年第1期25-30,共6页
In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetso... In the present paper, we construct the analytical exact solutions of some nonlinear evolution equations in mathematical physics; namely the space-time fractional Zakharov–Kuznetsov(ZK) and modified Zakharov–Kuznetsov(m ZK) equations by using fractional sub-equation method. As a result, new types of exact analytical solutions are obtained. The obtained results are shown graphically. Here the fractional derivative is described in the Jumarie's modified Riemann–Liouville sense. 展开更多
关键词 fractional sub-equation method space-time fractional Zakharov-Kuznetsov (ZK) equation space-time fractional modified Zakharov-Kuznetsov (mZK) equation modified Riemann-Liouvillederivative Mittag-leffler function
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New sub-equation method to construct solitons and other solutions for perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials 被引量:1
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作者 Elsayed M.E.Zayed Abdul-Ghani Al-Nowehy Reham M.A.Shohib 《Journal of Ocean Engineering and Science》 SCIE 2019年第1期14-23,共10页
In a previous work,Zayed and Al-Nowehy have applied the Riccati equation mapping method combined with the generalized extended(G/G)-expansion method and found new exact solutions of the nonlinear KPP equation.In the ... In a previous work,Zayed and Al-Nowehy have applied the Riccati equation mapping method combined with the generalized extended(G/G)-expansion method and found new exact solutions of the nonlinear KPP equation.In the present article,we propose a different method,namely,a new sub-equation method consists of the Riccati equation mapping method and the(G/G,1/G)-expansion method to find new exact solutions of the perturbed nonlinear Schrödinger equation with Kerr law nonlinearity in optical fiber materials.This proposed method is not found elsewhere.Hyperbolic,trigonometric and rational function solutions are given.New solutions of the generalized Riccati equation are presented for the first time which are not reported previously.The solutions of the given nonlinear equation can be applied in ocean engineering for calculating the height of tides in the ocean. 展开更多
关键词 New sub-equation method (G/G 1/G)-expansion method Generalized Riccati equation mapping method Perturbed nonlinear Schrödinger equation Exact solutions.
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IMPROVED FRACTIONAL SUB-EQUATION METHOD AND ITS APPLICATIONS TO FRACTIONAL PARTIAL DIFFERENTIAL EQUATIONS 被引量:1
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作者 Guoying Xu Tiecheng Xia 《Annals of Applied Mathematics》 2015年第3期354-362,共9页
Based on an improved fractional sub-equation method involving Jumarie's mo- dified Riemann-Liouville derivative, we construct analytical solutions of space-time fractional compound KdV-Burgers equation and coupled Bu... Based on an improved fractional sub-equation method involving Jumarie's mo- dified Riemann-Liouville derivative, we construct analytical solutions of space-time fractional compound KdV-Burgers equation and coupled Burgers' equations. These results not only reveal that the method is very effective and simple in studying solu- tions to the fractional partial differential equation, but also include some new exact solutions. 展开更多
关键词 improved fractional sub-equation method modified Riemann-Liouvillederivative fractional differential equation compound KdV-Burgers equation coupledBurgers' equations
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Travelling wave solutions of nonlinear conformable analytical approaches
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作者 Hira Tariq Hira Ashraf +1 位作者 Hadi Rezazadeh Ulviye Demirbilek 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2024年第3期502-518,共17页
The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling w... The presented study deals with the investigation of nonlinear Bogoyavlenskii equations with conformable time-derivative which has great importance in plasma physics and non-inspectoral scattering problems.Travelling wave solutions of this nonlinear conformable model are constructed by utilizing two powerful analytical approaches,namely,the modified auxiliary equation method and the Sardar sub-equation method.Many novel soliton solutions are extracted using these methods.Furthermore,3D surface graphs,contour plots and parametric graphs are drawn to show dynamical behavior of some obtained solutions with the aid of symbolic software such as Mathematica.The constructed solutions will help to understand the dynamical framework of nonlinear Bogoyavlenskii equations in the related physical phenomena. 展开更多
关键词 nonlinear partial differential equations modified auxiliary equation method Sardar sub-equation method soliton solutions
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Dynamics and Exact Solutions of (1 + 1)-Dimensional Generalized Boussinesq Equation with Time-Space Dispersion Term
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作者 Dahe Feng Jibin Li Jianjun Jiao 《Journal of Applied Mathematics and Physics》 2024年第8期2723-2737,共15页
We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of ... We study exact solutions to (1 + 1)-dimensional generalized Boussinesq equation with time-space dispersion term by making use of improved sub-equation method, and analyse the dynamical behavior and exact solutions of the sub-equation after constructing the nonlinear transformation and constraint conditions. Accordingly, we obtain twenty families of exact solutions such as analytical and singular solitons and singular periodic waves. In addition, we discuss the impact of system parameters on wave propagation. 展开更多
关键词 Generalized Boussinesq Equation Improved sub-equation Method BIFURCATION Soliton Solution Periodic Solution
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非线性分数阶演化方程的新解
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作者 刘银龙 夏铁成 刘泽宇 《上海大学学报(自然科学版)》 CAS CSCD 北大核心 2016年第4期469-476,共8页
通过使用改进的分数阶sub-equation方法寻求一些非线性分数阶演化方程的精确解,如分数阶Burgers方程、耦合分数阶Burgers方程与非线性分数阶Klein-Gordon方程等,并得到了这些非线性分数阶演化方程的新解.
关键词 改进的分数阶sub-equation方法 分数阶Burgers方程 耦合分数阶Burgers方程 分数阶Klein-Gordon方程
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New Analytical and Numerical Results For Fractional Bogoyavlensky-Konopelchenko Equation Arising in Fluid Dynamics 被引量:1
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作者 Ali Kurt 《Applied Mathematics(A Journal of Chinese Universities)》 SCIE CSCD 2020年第1期101-112,共12页
In this article,(2+1)-dimensional time fractional Bogoyavlensky-Konopelchenko(BK)equation is studied,which describes the interaction of wave propagating along the x axis and y axis.To acquire the exact solutions of BK... In this article,(2+1)-dimensional time fractional Bogoyavlensky-Konopelchenko(BK)equation is studied,which describes the interaction of wave propagating along the x axis and y axis.To acquire the exact solutions of BK equation we employed sub equation method that is predicated on Riccati equation,and for numerical solutions the residual power series method is implemented.Some graphical results that compares the numerical and analytical solutions are given for di erent values of.Also comparative table for the obtained solutions is presented. 展开更多
关键词 Conformable Fractional Derivative Fractional Bogoyavlensky-Konopelchenko Equation sub-equation Method Residual Power Series Method
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On Exact Traveling Wave Solutions for (1 + 1) Dimensional Kaup-Kupershmidt Equation
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作者 Dahe Feng Kezan Li 《Applied Mathematics》 2011年第6期752-756,共5页
In this present paper, the Fan sub-equation method is used to construct exact traveling wave solutions of the (1 + 1) dimensional Kaup-Kupershmidt equation. Many exact traveling wave solutions are successfully obtaine... In this present paper, the Fan sub-equation method is used to construct exact traveling wave solutions of the (1 + 1) dimensional Kaup-Kupershmidt equation. Many exact traveling wave solutions are successfully obtained, which contain solitary wave solutions, trigonometric function solutions, hyperbolic function solutions and Jacobian elliptic function periodic solutions with double periods. 展开更多
关键词 FAN sub-equation Method Kaup-Kupershmidt EQUATION EXACT TRAVELING Wave Solutions
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New solutions for four novel generalized nonlinear fractional fifth-order equations
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作者 Mehmet Senol Lanre Akinyemi +1 位作者 Henrietta Nkansah Waleed Adel 《Journal of Ocean Engineering and Science》 SCIE 2024年第1期59-65,共7页
In this paper,new four fifth-order fractional nonlinear equations are derived and investigated.The frac-tional terms are defined in the conformable sense and these equations are then solved using two effective methods... In this paper,new four fifth-order fractional nonlinear equations are derived and investigated.The frac-tional terms are defined in the conformable sense and these equations are then solved using two effective methods,namely,the sub-equation and the generalized Kudryashov methods.These methods were tested on the proposed models and succeeded in finding new solutions with different values of parameters.A graphical representation of some results is provided and proves the efficiency and applicability of the proposed methods for providing solutions with known physical behavior.These methods are good candi-dates for solving other similar problems in the future. 展开更多
关键词 Conformable derivative Generalized Kudryashov method sub-equation method Riccati equation SOLITONS
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A novel approach to study generalized coupled cubic Schrödinger-Korteweg-de Vries equations
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作者 Lanre Akinyemi P.Veeresha +3 位作者 M.T.Darvishi Hadi Rezazadeh Mehmet Senol Udoh Akpan 《Journal of Ocean Engineering and Science》 SCIE 2024年第1期13-24,共12页
The Kortewegde Vries(KdV)equation represents the propagation of long waves in dispersive media,whereas the cubic nonlinear Schrödinger(CNLS)equation depicts the dynamics of narrow-bandwidth wave packets consistin... The Kortewegde Vries(KdV)equation represents the propagation of long waves in dispersive media,whereas the cubic nonlinear Schrödinger(CNLS)equation depicts the dynamics of narrow-bandwidth wave packets consisting of short dispersive waves.A model that couples these two equations seems in-triguing for simulating the interaction of long and short waves,which is important in many domains of applied sciences and engineering,and such a system has been investigated in recent decades.This work uses a modified Sardar sub-equation procedure to secure the soliton-type solutions of the generalized cubic nonlinear Schrödinger-Korteweg-de Vries system of equations.For various selections of arbitrary parameters in these solutions,the dynamic properties of some acquired solutions are represented graph-ically and analyzed.In particular,the dynamics of the bright solitons,dark solitons,mixed bright-dark solitons,W-shaped solitons,M-shaped solitons,periodic waves,and other soliton-type solutions.Our re-sults demonstrated that the proposed technique is highly efficient and effective for the aforementioned problems,as well as other nonlinear problems that may arise in the fields of mathematical physics and engineering. 展开更多
关键词 CNLS equation Modified Sardar sub-equation method KdV equation SOLITONS Long and short waves
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Investigation of soliton solutions with different wave structures to the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation 被引量:5
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作者 M S Osman K U Tariq +4 位作者 Ahmet Bekir A Elmoasry Nasser S Elazab M Younis Mahmoud Abdel-Aty 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第3期7-13,共7页
The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets... The principal objective of this article is to construct new and further exact soliton solutions of the(2+1)-dimensional Heisenberg ferromagnetic spin chain equation which investigates the nonlinear dynamics of magnets and explains their ordering in ferromagnetic materials.These solutions are exerted via the new extended FAN sub-equation method.We successfully obtain dark,bright,combined bright-dark,combined dark-singular,periodic,periodic singular,and elliptic wave solutions to this equation which are interesting classes of nonlinear excitation presenting spin dynamics in classical and semi-classical continuum Heisenberg systems.3D figures are illustrated under an appropriate selection of parameters.The applied technique is suitable to be used in gaining the exact solutions of most nonlinear partial/fractional differential equations which appear in complex phenomena. 展开更多
关键词 SOLITON solutions HEISENBERG FERROMAGNETIC EQUATION FAN sub-equation method
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Two effective approaches for solving fractional generalized Hirota-Satsuma coupled KdV system arising in interaction of long waves 被引量:3
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作者 Ali Kurt Hadi Rezazadeh +4 位作者 Mehmet Senol Ahmad Neirameh Orkun Tasbozan Mostafa Eslami Mohammad Mirzazadeh 《Journal of Ocean Engineering and Science》 SCIE 2019年第1期24-32,共9页
In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,whic... In this article,two different methods,namely sub-equation method and residual power series method,have been used to obtain new exact and approximate solutions of the generalized Hirota-Satsuma system of equations,which is a coupled KdV model.The fractional derivative is taken in the conformable sense.Each of the obtained exact solutions were checked by substituting them into the corresponding system with the help of Maple symbolic computation package.The results indicate that both methods are easy to implement,effective and reliable.They are therefore ready to apply for various partial fractional differential equations. 展开更多
关键词 Hirota-Satsuma coupled KdV system sub-equation method Power series method Conformable fractional derivative
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Multiple-solitons for generalized(2+1)-dimensional conformable Korteweg-de Vries-Kadomtsev-Petviashvili equation 被引量:1
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作者 Lanre Akinyemi Mehmet Senol +1 位作者 Orkun Tasbozan Ali Kurt 《Journal of Ocean Engineering and Science》 SCIE 2022年第6期536-542,共7页
This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Pe... This paper studied new class of integral equation called the Korteweg-de Vries-Kadomtsev-Petviashvili(KdV-KP)equation.This equation consist of the well-known fifth-order KdV equation in the context of the Kadomtsev-Petviashvili equation.The newly gathered class of sixth-order KdV-KP equation is studied using the sub-equation method to obtain several soliton-type solutions which consist of trigonometric,hyperbolic,and rational solutions.The application of the sub-equation approach in this work draws attention to the outstanding characteristics of the suggested method and its ability to handle completely integrable equations.Furthermore,the obtained solutions have not been reported in the previous literature and might have significant impact on future research. 展开更多
关键词 Conformable derivative sub-equation method KdV-KP equations Multiple-soliton solutions
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Modulation instability analysis, optical and other solutions to the modified nonlinear Schr?dinger equation
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作者 Muhammad Younis Tukur Abdulkadir Sulaiman +2 位作者 Muhammad Bilal Shafqat Ur Rehman Usman Younas 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第6期1-12,共12页
This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrodinger equation,which models the propagation of rogue waves in ocean engineering.The extended Fan sub-equation met... This paper studies the new families of exact traveling wave solutions with the modified nonlinear Schrodinger equation,which models the propagation of rogue waves in ocean engineering.The extended Fan sub-equation method with five parameters is used to find exact traveling wave solutions.It has been observed that the equation exhibits a collection of traveling wave solutions for limiting values of parameters.This method is beneficial for solving nonlinear partial differential equations,because it is not only useful for finding the new exact traveling wave solutions,but also gives us the solutions obtained previously by the usage of other techniques(Riccati equation,or first-kind elliptic equation,or the generalized Riccati equation as mapping equation,or auxiliary ordinary differential equation method)in a combined approach.Moreover,by means of the concept of linear stability,we prove that the governing model is stable.3 D figures are plotted for showing the physical behavior of the obtained solutions for the different values of unknown parameters with constraint conditions. 展开更多
关键词 optical soliton MNLSE stability analysis generalized elliptic equation extended Fan sub-equation method
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Analytical and approximate solutions of(2+1)-dimensional time-fractional Burgers-Kadomtsev-Petviashvili equation
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作者 Mehmet Senol 《Communications in Theoretical Physics》 SCIE CAS CSCD 2020年第5期21-31,共11页
In this paper,we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation,namely Burgers-Kadomtsev-Petviashvili equation(Burger... In this paper,we applied the sub-equation method to obtain a new exact solution set for the extended version of the time-fractional Kadomtsev-Petviashvili equation,namely Burgers-Kadomtsev-Petviashvili equation(Burgers-K-P)that arises in shallow water waves.Furthermore,using the residual power series method(RPSM),approximate solutions of the equation were obtained with the help of the Mathematica symbolic computation package.We also presented a few graphical illustrations for some surfaces.The fractional derivatives were considered in the conformable sense.All of the obtained solutions were replaced back in the governing equation to check and ensure the reliability of the method.The numerical outcomes confirmed that both methods are simple,robust and effective to achieve exact and approximate solutions of nonlinear fractional differential equations. 展开更多
关键词 fractional partial differential equations Burgers-Kadomtsev-Petviashvili equation conformable fractional derivative sub-equation method residual power series method
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New Exact Solutions for the Wick-Type Stochastic Kudryashov–Sinelshchikov Equation
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作者 S.Saha Ray S.Singh 《Communications in Theoretical Physics》 SCIE CAS CSCD 2017年第2期197-206,共10页
In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stoch... In this article, exact solutions of Wick-type stochastic Kudryashov–Sinelshchikov equation have been obtained by using improved Sub-equation method. We have used Hermite transform for transforming the Wick-type stochastic Kudryashov–Sinelshchikov equation to deterministic partial differential equation. Also we have applied inverse Hermite transform for obtaining a set of stochastic solutions in the white noise space. 展开更多
关键词 Kudryashov–Sinelshchikov Wick-product White noise space improved sub-equation method Hermite transform inverse Hermite transform
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