Papers by Mariyam Mushtaq
New trends in mathematical sciences, Oct 20, 2017
This paper obtains the solitary wave solutions of two different forms of Boussinesq equations tha... more This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He's polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations.
Universal journal of computational mathematics, Feb 1, 2015
In this research paper, we applied the Adomian's decomposition method to determine the analytical... more In this research paper, we applied the Adomian's decomposition method to determine the analytical exact solutions of linear and nonlinear Goursat problems which play very important part in applied and engineering sciences. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Some examples with closed form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.
New Trends in Mathematical Science, 2017
This paper obtains the solitary wave solutions of two different forms of Boussinesq equations tha... more This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He's polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations.
Mathematical theory and modeling, 2016
This paper obtains the solitary wave solutions of two different forms of Boussinesq equations tha... more This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He’s polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations. Keywords: Decomposition Method, He’s polynomials, cubic Boussinesq equation, Coupled Boussinesq equations
Universal Journal of Computational Mathematics, 2015
In this research paper, we applied the Adomian's decomposition method to determine the analytical... more In this research paper, we applied the Adomian's decomposition method to determine the analytical exact solutions of linear and nonlinear Goursat problems which play very important part in applied and engineering sciences. The proposed technique is fully compatible with the complexity of these problems and obtained results are highly encouraging. Some examples with closed form solutions are studied in detail to further illustrate the proposed technique, and the results obtained indicate this approach is indeed practical and efficient.
Mathematical theory and modeling, 2016
This paper obtains the solitary wave solutions of two different forms of Boussinesq equations tha... more This paper obtains the solitary wave solutions of two different forms of Boussinesq equations that model the study of shallow water waves in lakes and ocean beaches. The decomposition method using He's polynomials is applied to solve the governing equations. The travelling wave hypothesis is also utilized to solve the generalized case of coupled Boussinesq equations, and, thus, an exact soliton solution is obtained. The results are also supported by numerical simulations.
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Papers by Mariyam Mushtaq