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Waves in Random and Complex Media Volume 21, 2011 - Issue 4
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Original Articles

Analytical and numerical solutions to the Davey–Stewartson equation with power-law nonlinearity

Ghodrat Ebadi Faculty of Mathematical Sciences, University of Tabriz, Tabriz 51666-14766, Iran
,
E.V. Krishnan Department of Mathematics and Statistics, Sultan Qaboos University, P.O. Box 36, Muscat, Al Khod 123, Sultanate of Oman
,
Manel Labidi Laboratory of Engineering Mathematics, Tunisia Polytechnic School, University of 7th November at Carthage, BP 743, La Marsa 2070, Tunisia
,
Essaid Zerrad Department of Physics and Pre-Engineering, Delaware State University, Dover, DE 19901-2277, USA
&
Anjan Biswas Department of Mathematical Sciences, Delaware State University, Dover, DE 19901-2277, USACorrespondence[email protected]
Pages 559-590 | Received 10 Jan 2011, Accepted 07 Jul 2011, Published online: 18 Aug 2011

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S. M. Mabrouk, E. Y. Abu El Seoud & Abdul-Majid Wazwaz. (2022) The nonlocal potential transformation method for solitary wave packets of a shock-breaking dynamics system. Waves in Random and Complex Media 0:0, pages 1-14.
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S. Sarwar & M. M. Rashidi. (2016) Approximate solution of two-term fractional-order diffusion, wave-diffusion, and telegraph models arising in mathematical physics using optimal homotopy asymptotic method. Waves in Random and Complex Media 26:3, pages 365-382.
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Urooj Akram, Aly. R. Seadawy, Syed T. R. Rizvi, Muhammad Younis & Ali Althobaiti. (2021) Some new dispersive dromions and integrability analysis for the Davey–Stewartson (DS-II) model in fluid dynamics. Modern Physics Letters B 36:02.
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Ni Song, Xiao Ying Zhao & Yu Xiang Lei. (2021) Dynamical behaviors of optical soliton for integrable three-component coupled nonlinear Schrödinger equation. Optik 242, pages 167092.
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Saima Arshed, Nauman Raza & Monairah Alansari. (2021) Soliton solutions of the generalized Davey-Stewartson equation with full nonlinearities via three integrating schemes. Ain Shams Engineering Journal 12:3, pages 3091-3098.
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Tukur Abdulkadir Sulaiman, Hasan Bulut & Haci Mehmet Baskonus. (2021) On the exact solutions to some system of complex nonlinear models. Applied Mathematics and Nonlinear Sciences 6:1, pages 29-42.
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Kwasi Boateng, Weiguo Yang, Wilson Osafo Apeanti & David Yaro. (2019) New Exact Solutions and Modulation Instability for the Nonlinear (2+1)-Dimensional Davey-Stewartson System of Equation. Advances in Mathematical Physics 2019, pages 1-15.
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Yali Gao, Liquan Mei & Rui Li. (2018) Galerkin methods for the Davey–Stewartson equations. Applied Mathematics and Computation 328, pages 144-161.
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Ehab S. Selima, Yadan Mao, Xiaohua Yao, Adel M. Morad, Talaat Abdelhamid & Basem I. Selim. (2018) Applicable symbolic computations on dynamics of small-amplitude long waves and Davey–Stewartson equations in finite water depth. Applied Mathematical Modelling 57, pages 376-390.
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Laurent Vuillon, Denys Dutykh & Francesco Fedele. (2018) Some special solutions to the Hyperbolic NLS equation. Communications in Nonlinear Science and Numerical Simulation 57, pages 202-220.
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Hui-Qin Hao, Rui Guo & Jian-Wen Zhang. (2017) Modulation instability, conservation laws and soliton solutions for an inhomogeneous discrete nonlinear Schrödinger equation. Nonlinear Dynamics 88:3, pages 1615-1622.
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Seyma Tuluce Demiray & Hasan Bulut. (2017) New soliton solutions of Davey–Stewartson equation with power-law nonlinearity. Optical and Quantum Electronics 49:3.
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A. Akgül, M. S. Hashemi, M. Inc & S. A. Raheem. (2016) Constructing two powerful methods to solve the Thomas–Fermi equation. Nonlinear Dynamics 87:2, pages 1435-1444.
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Haci Mehmet Baskonus. (2016) New acoustic wave behaviors to the Davey–Stewartson equation with power-law nonlinearity arising in fluid dynamics. Nonlinear Dynamics 86:1, pages 177-183.
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Ji-Huan He. (2015) Maximal Thermo-geometric Parameter in a Nonlinear Heat Conduction Equation. Bulletin of the Malaysian Mathematical Sciences Society 39:2, pages 605-608.
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Yali Gao, Liquan Mei & Rui Li. (2015) A time-splitting Galerkin finite element method for the Davey–Stewartson equations. Computer Physics Communications 197, pages 35-42.
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M. Mirzazadeh. (2015) Soliton solutions of Davey–Stewartson equation by trial equation method and ansatz approach. Nonlinear Dynamics 82:4, pages 1775-1780.
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Y. Gurefe, E. Misirli, Y. Pandir, A. Sonmezoglu & M. Ekici. (2014) New Exact Solutions of the Davey–Stewartson Equation with Power-Law Nonlinearity. Bulletin of the Malaysian Mathematical Sciences Society 38:3, pages 1223-1234.
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M.A. Mohamed & M.Sh. Torky. (2014) A comparative study of numerical methods for solving the generalized Ito system. Journal of the Egyptian Mathematical Society 22:1, pages 102-114.
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Zainab Ayati. (2014) Comparing between G′/G expansion method and tanh-method. Open Engineering 4:4.
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Mostafa Eslami & Mohammad Mirzazadeh. (2013) Topological 1-soliton solution of nonlinear Schrödinger equation with dual-power law nonlinearity in nonlinear optical fibers. The European Physical Journal Plus 128:11.
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Rui Guo, Hui-Qin Hao & Ling-Ling Zhang. (2013) Dynamic behaviors of the breather solutions for the AB system in fluid mechanics. Nonlinear Dynamics 74:3, pages 701-709.
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A NAZARZADEH, M ESLAMI & M MIRZAZADEH. (2013) Exact solutions of some nonlinear partial differential equations using functional variable method. Pramana 81:2, pages 225-236.
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Honglei Wang & Chunhuan Xiang. (2013) Jacobi elliptic function solutions for the modified Korteweg–de Vries equation. Journal of King Saud University - Science 25:3, pages 271-274.
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A.H. Bhrawy, M.A. Abdelkawy & Anjan Biswas. (2013) Cnoidal and snoidal wave solutions to coupled nonlinear wave equations by the extended Jacobi’s elliptic function method. Communications in Nonlinear Science and Numerical Simulation 18:4, pages 915-925.
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Mostafa Eslami & Mohammad Mirzazadeh. (2013) Functional variable method to study nonlinear evolution equations. Open Engineering 3:3.
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Houria Triki,Daniela M. Milovic,T. Hayat,Omar M. Aldossary,Anjan Biswas,. (2011) Topological Soliton Solutions of .2 C 1/-dimensional KdV Equation with Power Law Nonlinearity and Time-dependent Coefficients. International Journal of Nonlinear Sciences and Numerical Simulation 12:1-8, pages 35-43.
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