Hasibun Naher
Universiti Sains Malaysia, School of Mathematical Sciences, Department Member
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In this work, the second order nonlinear ordinary differential equation is implemented as an auxiliary equation. For illustration, the generalized Hirota-Satsuma coupled KdV equations are considered for constructing traveling wave... more
In this work, the second order nonlinear ordinary differential equation is implemented as an auxiliary equation. For illustration, the generalized Hirota-Satsuma coupled KdV equations are considered for constructing traveling wave solutions by applying a new extension of so called ( )
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In this study, numerical prediction of surge associated with a storm is made through finite difference method accurately incorporating the coastal complexities along the coast of Bangladesh. In incorporating the coastal complexities with... more
In this study, numerical prediction of surge associated with a storm is made through finite difference method accurately incorporating the coastal complexities along the coast of Bangladesh. In incorporating the coastal complexities with a considerable accuracy, (1/120) grid resolution is used. To incorporate river dynamics, the fresh water discharge through the Meghna River is taken into account. Simulated results by the study are found to be in good agreement with the available observations and reported data. For better forecasting, estimation of flooding is of importance, which is responsible for most death. Thus, the main objective of this paper is to develop an effective numerical model that will help to reduce the death during storm surges along the coastal area of Bangladesh.
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The generalized and improved G0=Gð Þ-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the... more
The generalized and improved G0=Gð Þ-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.
In this article, the improved ( ) / GG ' -expansion method has been implemented to generate travelling wave solutions, where ( ) G ξ satisfies the second order linear ordinary differential equation. To show the advantages of the... more
In this article, the improved ( ) / GG ' -expansion method has been implemented to generate travelling wave solutions, where ( ) G ξ satisfies the second order linear ordinary differential equation. To show the advantages of the method, the (3+1)-dimensional Kadomstev-Petviashvili (KP) equation has been investigated. Higher- dimensional nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation. Also, in order to understand the behaviour of solutions, the graphical representations of some obtained solutions have been presented.
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The improved (G’/G)-expansion method is a powerful mathematical tool for solving nonlinear evolution equations whicharise in mathematical physics, engineering sciences and other technical arena. In this article, we construct some new... more
The improved (G’/G)-expansion method is a powerful mathematical tool for solving nonlinear evolution equations whicharise in mathematical physics, engineering sciences and other technical arena. In this article, we construct some new exact travelingwave solutions for the modified Benjamin-Bona-Mahony equation by applying the improved (G’/G)-expansion method. In themethod, the general solution of the second order linear ordinary differential equation with constant coefficients is used for studyingnonlinear partial differential equations. The solution procedure of this method is executed by algebraic software, such as, Maple. Theobtained solutions including solitary and periodic wave solutions are presented in terms of the hyperbolic function, the trigonometricfunction and the rational forms. It is noteworthy to reveal that some of our solutions are in good agreement with the published resultsfor special cases which certifies our other solutions. Furthermore, the graphical presentatio...
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The improved (G’/G)-expansion method is a powerful mathematical tool for solving nonlinear evolution equations whicharise in mathematical physics, engineering sciences and other technical arena. In this article, we construct some new... more
The improved (G’/G)-expansion method is a powerful mathematical tool for solving nonlinear evolution equations whicharise in mathematical physics, engineering sciences and other technical arena. In this article, we construct some new exact travelingwave solutions for the modified Benjamin-Bona-Mahony equation by applying the improved (G’/G)-expansion method. In themethod, the general solution of the second order linear ordinary differential equation with constant coefficients is used for studyingnonlinear partial differential equations. The solution procedure of this method is executed by algebraic software, such as, Maple. Theobtained solutions including solitary and periodic wave solutions are presented in terms of the hyperbolic function, the trigonometricfunction and the rational forms. It is noteworthy to reveal that some of our solutions are in good agreement with the published resultsfor special cases which certifies our other solutions. Furthermore, the graphical presentatio...
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We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation by the -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave... more
We construct the traveling wave solutions of the fifth-order Caudrey-Dodd-Gibbon (CDG) equation by the -expansion method. Abundant traveling wave solutions with arbitrary parameters are successfully obtained by this method and the wave solutions are expressed in terms of the hyperbolic, the trigonometric, and the rational functions. It is shown that the -expansion method is a powerful and concise mathematical tool for solving nonlinear partial differential equations.
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we apply the improved(G′/G)-expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition,G″+λG′+μG=0together withb(α)=∑q=−wwpq(G′/G)qis employed... more
we apply the improved(G′/G)-expansion method for constructing abundant new exact traveling wave solutions of the (2+1)-dimensional Modified Zakharov-Kuznetsov equation. In addition,G″+λG′+μG=0together withb(α)=∑q=−wwpq(G′/G)qis employed in this method, wherepq(q=0,±1,±2,…,±w),λandμare constants. Moreover, the obtained solutions including solitons and periodic solutions are described by three different families. Also, it is noteworthy to mention out that, some of our solutions are coincided with already published results, if parameters taken particular values. Furthermore, the graphical presentations are demonstrated for some of newly obtained solutions.
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This article was published in the UPB Scientific Bulletin, Series A: Applied Mathematics and Physics [© 2014 Politechnica University of Bucharest ] The Journal's website is at:... more
This article was published in the UPB Scientific Bulletin, Series A: Applied Mathematics and Physics [© 2014 Politechnica University of Bucharest ] The Journal's website is at: http://www.scientificbulletin.upb.ro/rev_docs_arhiva/full78d_557338.pdf
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In this article, the improved ()/G G ′-expansion method has been implemented to generate travelling wave solutions, where ()G ξ satisfies the second order linear ordinary differential equation. To show the advantages of the method, the... more
In this article, the improved ()/G G ′-expansion method has been implemented to generate travelling wave solutions, where ()G ξ satisfies the second order linear ordinary differential equation. To show the advantages of the method, the (3+1)-dimensional Kadomstev-Petviashvili (KP) equation has been investigated. Higher-dimensional nonlinear partial differential equations have many potential applications in mathematical physics and engineering sciences. Some of our solutions are in good agreement with already published results for a special case and others are new. The solutions in this work may express a variety of new features of waves. Furthermore, these solutions can be valuable in the theoretical and numerical studies of the considered equation. Also, in order to understand the behaviour of solutions, the graphical representations of some obtained solutions have been presented.
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In this article, simplified Modified Camassa-Holm (SMCH) equation is investigated to construct some new analytical solutions via the improved '/G G-expansion method. Second order linear ordinary differential equation is used with... more
In this article, simplified Modified Camassa-Holm (SMCH) equation is investigated to construct some new analytical solutions via the improved '/G G-expansion method. Second order linear ordinary differential equation is used with constant coefficients in the method. As a result, some new travelling wave solutions are obtained through the hyperbolic function, the trigonometric function and the rational forms. If parameters take specific values, the solitary waves are derives from the travelling waves. Furthermore, some of the solutions are presented in the figures with the aid of commercial software Maple.
This article was published in the Applied Mathematical Sciences [© 2012 Hasibun Naher and Farah Aini Abdullah.] The Journal's website is at:http://www.m-hikari.com/ams/ams-2012/ams-109-112-2012/naherAMS109-112-2012.pdf
The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial... more
The present study investigates the lump, one-stripe, lump-stripe, and breather wave solutions to the (2+1)dimensional Sawada-Kotera equation using the Hirota bilinear method. For lump and lump-stripe solutions, a quadratic polynomial function, and a quadratic polynomial function in conjunction with an exponential term are assumed for the unknown function giving the solution to the mentioned equation, respectively. On the other hand, only an exponential function is considered for one-stripe solutions. Besides, the homoclinic test approach is adopted for constructing breather wave solutions. The propagations of the attained lump, lump-stripe, and breather wave solutions are shown through some graphical illustrations. The graphical outputs demonstrate that the lump wave moves along the straight line = − and exponentially decreases away from the origin of the spatial domain. On the other hand, lump-kink solutions illustrate the fission and fusion interaction behaviors upon the selection of the free parameters. Fission and fusion processes show that the stripe soliton splits into a stripe soliton and a lump soliton, and then the lump soliton merges into one stripe soliton. In addition, the achieved breather waves illustrate the periodic behaviors in the-plane. The outcomes of the study can be useful for a better understanding of the physical nature of long waves in shallow water under gravity.
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Bangladesh is one of the most vulnerable countries in the world with around 718,000 deaths in the past fifty years. This country is especially in danger for cyclones because of its location in the triangular-shaped Bay of Bengal. The... more
Bangladesh is one of the most vulnerable countries in the world with around 718,000 deaths in the past fifty years. This country is especially in danger for cyclones because of its location in the triangular-shaped Bay of Bengal. The scientific scenario suggests that enlarged sea surface temperature will intensify cyclone movement. Tropical cyclones generate storm surges. Storm surges severely change the coastal environment, damage coastal structures, destroy forests and crops, inundate the coastline with saltwater and cause loss of lives. Due to overcrowding in the mainland in Bangladesh, poor and landless people live on the coast and they face frequent cyclones and associated surges. They affect food and drinking water and there is danger of transmission risks of infectious diseases, such as diarrhea, malaria, eye infections, skin diseases, etc. Some problems following a cyclone are usually created for their low literacy rate and poor knowledge of the environment. The tangible mon...
We have generated many new non-travelling wave solutions by executing the new extended generalized and improved (G'/G)-Expansion Method. Here the nonlinear ordinary differential equation with many new and real parameters has been used... more
We have generated many new non-travelling wave solutions by executing the new extended generalized and improved (G'/G)-Expansion Method. Here the nonlinear ordinary differential equation with many new and real parameters has been used as an auxiliary equation. We have investigated the Fisher equation to show the advantages and effectiveness of this method. The obtained non-travelling solutions are expressed through the hyperbolic functions, trigonometric functions and rational functional forms. Results showing that the method is concise, direct and highly effective to study nonlinear evolution equations those are in mathematical physics and engineering.
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In this article, simplified Modified Camassa-Holm (SMCH) equation is investigated to construct some new analytical solutions via the improved '/ GG-expansion method. Second order linear ordinary differential equation is used with... more
In this article, simplified Modified Camassa-Holm (SMCH) equation is investigated to construct some new analytical solutions via the improved '/ GG-expansion method. Second order linear ordinary differential equation is used with constant coefficients in the method. As a result, some new travelling wave solutions are obtained through the hyperbolic function, the trigonometric function and the rational forms. If parameters take specific values, the solitary waves are derives from the travelling waves. Furthermore, some of the solutions are presented in the figures with the aid of commercial software Maple.
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The generalized Riccati equation mapping is extended together with the () / G G ′ -expansion method and is a powerful mathematical tool for solving nonlinear partial differential equations. In this article, we construct twenty seven new... more
The generalized Riccati equation mapping is extended together with the () / G G ′ -expansion method and is a powerful mathematical tool for solving nonlinear partial differential equations. In this article, we construct twenty seven new exact traveling wave solutions including solitons and periodic solutions of the modified Benjamin-Bona-Mahony equation by applying the extended generalized Riccati equation mapping method. In this method, () () () 2 G p rG sG μ μ μ ′ = + + is implemented as the auxiliary equation, where , r s and p are arbitrary constants and called the generalized Riccati equation. The obtained solutions are described in four different families including the hyperbolic functions, the trigonometric functions and the rational functions. In addition, it is worth mentioning that one of newly obtained solutions is identical for a special case with already published result which validates our other solutions. Keywords: The modified Benjamin-Bona-Mahony equation, the gener...
In this article, we generate abundant traveling wave solutions of partial differential equation, namely, the (2+1)-dimensional breaking soliton equation involving parameter by applying the improved (G'/G) -expansion method. In this... more
In this article, we generate abundant traveling wave solutions of partial differential equation, namely, the (2+1)-dimensional breaking soliton equation involving parameter by applying the improved (G'/G) -expansion method. In this method, G″+ψG′+ФG=0 together with (formula presented) is implemented, where Sf(f = 0,±1,±2,...,±U, ψ and Ф are constants. In addition, the obtained analytical solutions are illustrated in three different families including solitons and periodic solurions. Further, it is vital mentioning that, for a special case, some of our solutions are in good contract with those gained by other authors.
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ABSTRACT In this article, an improved (G′/G)-expansion method is implemented for the simplified Modified Camassa-Holm (MCH) equation involving parameters, with an aim to construct many new traveling wave solutions. In this method, second... more
ABSTRACT In this article, an improved (G′/G)-expansion method is implemented for the simplified Modified Camassa-Holm (MCH) equation involving parameters, with an aim to construct many new traveling wave solutions. In this method, second order linear ordinary differential equation with constant coefficients has been implemented as an auxiliary equation. The generated solutions including solitons and periodic solutions are demonstrated by the hyperbolic function, the trigonometric function and the rational forms. If the parameters take particular values, the solutions become in special functional form. Moreover, it is worth mentioning that, some of our solutions are in good agreement with already published results in the open literature by setting appropriate values of constants, which proves our other solutions. In addition, some of obtained solutions are described in the figures with the aid of commercial software Maple 13.
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The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate... more
The generalized and improved (G'/G)-expansion method is a powerful and advantageous mathematical tool for establishing abundant new traveling wave solutions of nonlinear partial differential equations. In this article, we investigate the higher dimensional nonlinear evolution equation, namely, the (3+1)-dimensional modified KdV-Zakharov-Kuznetsev equation via this powerful method. The solutions are found in hyperbolic, trigonometric and rational function form involving more parameters and some of our constructed solutions are identical with results obtained by other authors if certain parameters take special values and some are new. The numerical results described in the figures were obtained with the aid of commercial software Maple.
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... Academic Editor: Jun-Juh Yan. ... Zayed and Al-Joudi [51] concerned about the method to find solutions of the NLPDEs in mathematical physics and so on ... Step 2. Suppose that the traveling wave solution of (2.3) can be presented in... more
... Academic Editor: Jun-Juh Yan. ... Zayed and Al-Joudi [51] concerned about the method to find solutions of the NLPDEs in mathematical physics and so on ... Step 2. Suppose that the traveling wave solution of (2.3) can be presented in the following form [52]: 𝑣 ( 𝜂 ) = 𝑚 𝑗 = − 𝑚 𝑎 𝑗 ...
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ABSTRACT The generalized Riccati equation mapping is extended with the basic (G′/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct... more
ABSTRACT The generalized Riccati equation mapping is extended with the basic (G′/G)-expansion method which is powerful and straightforward mathematical tool for solving nonlinear partial differential equations. In this paper, we construct twenty-seven traveling wave solutions for the (2+1)-dimensional modified Zakharov-Kuznetsov equation by applying this method. Further, the auxiliary equation G′(η)=w+uG(η)+vG2(η) is executed with arbitrary constant coefficients and called the generalized Riccati equation. The obtained solutions including solitons and periodic solutions are illustrated through the hyperbolic functions, the trigonometric functions, and the rational functions. In addition, it is worth declaring that one of our solutions is identical for special case with already established result which verifies our other solutions. Moreover, some of obtained solutions are depicted in the figures with the aid of Maple.