Novel solitons and periodic wave solutions for Davey–Stewartson system with variable coefficients

El-Shiekh, Rehab M.; Gaballah, Mahmoud

doi:10.1080/16583655.2020.1774975

Cited by 18 publications

(3 citation statements)

References 42 publications

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“…Recently, many new methods have been constructed to obtain new solutions for nonlinear partial differential equations like symmetry groups, tanh method, trial equation method, sin-Gordon equation method, etc. (Chen et al 2019(Chen et al , 2020Hua et al 2019;Liu et al 2019;Mao et al 2019;Xia et al 2020;Xu et al 2020) (El-Sayed et al 2015, 2014, 2021, 2018aEl-Shiekh and Rehab 2018b;El-Shiekh 2017, 2015, 2013El-Shiekh and Gaballah 2020b;Moatimid et al 2013;Moussa et al 2012;El-Shiekh 2010, 2011;Moatimid and El Shikh 2008;Moussa and El Shikh 2006;Chen et al 2021;He et al 2021;Lü and Ma 2016;Xia et al 2020;Yin et al 2020).…”

Section: Direct Similarity Reductionmentioning

confidence: 99%

“…In the following we are going to apply one of the similarity techniques, the direct similarity reduction method (El-Shiekh 2019, 2017, 2015, 2013, 2018aEl-Shiekh and Gaballah 2020b;El-Shiekh 2008, 2011) where ′ denotes the derivative with respect to . Collect the U coefficient and its derivatives, also, the real and imaginary parts together, assuming that e i( (z,t)) ≠ 0, we have…”

Section: Direct Similarity Reductionmentioning

confidence: 99%

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New rogon waves for the nonautonomous variable coefficients Schrö dinger equation

El-Shiekh

Gaballah

2021

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In this study, the nonautonomous variable coefficients Schrödinger equation describes rogon waves in ocean dynamics and optics, is reduced to the nonlinear ordinary differential equation by using the direct similarity technique. The reduced equation is a Riccati equation of Jacobi elliptic wave type solutions. Therefore, many new Jacobi elliptic wave, periodic and hyperbolic wave solutions are obtained for the nonautonomous variable coefficients Schrödinger equation with some constraints between the variable coefficients. Moreover, a rational solution is given. Finally, many plots for the new rogon wave solutions are investigated.

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Section: Direct Similarity Reductionmentioning

confidence: 99%

Section: Direct Similarity Reductionmentioning

confidence: 99%

New rogon waves for the nonautonomous variable coefficients Schrö dinger equation

El-Shiekh

Gaballah

2021

Opt Quant Electron

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“…This equation has great importance in physical phenomena and some important applications include numerical forecasting, optical fibres, nonlinear optics, quantum field theory, etc. [4][5][6][7][8][9][10][11][12]. Particularly, two-dimensional SGE can be used for identifying Josephson-junction model in quantum tunnelling [13].…”

Section: Introductionmentioning

confidence: 99%

Application of DRBEM for 2D sine-Gordon equation

Alsoy-Akgün

2021

Journal of Taibah University for Science

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This research paper introduces an application of dual reciprocity boundary element method (DRBEM) for the solution of sine-Gordon equation (SGE) in two-space dimension. Initially, the time derivatives are expanded using central difference schemes. After inserting the finite difference approximations into the governing equation, the pattern of the modified Helmholtz equation is obtained. The fundamental solution of modified Helmholtz equation is employed in the integral equation formulation. The inhomogeneous terms of the equation cause a domain integral in the integral equation formulation which leads to loss of advantage of the method. The DRBEM provides to transform the domain integral into the boundary integral by approximating the inhomogeneous term of the equation with thin plate spline (r 2 ln r). First, code validation of the procedure is done using a test problem and then proposed method is applied for several cases involving line and ring solitons to display its capacity to treat the problem. Presented numerical results are observed to be in good agreement with other numerical results available in the literature.

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Novel nonlinear quantum dust acoustic waves for modified variable coefficients Zakharove–Kusnetsov equation in dusty plasma

Gaballah,

El‐Shiekh

2024

Math Methods in App Sciences

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In this paper, the direct similarity reduction method is used to reduce the modified variable coefficient Zakharove–Kusnetsov equation (vcmZK), which represents the propagation of quantum dust acoustic waves (QDAWs) in an inhomogeneous magnetized dusty plasma field, into a nonlinear ordinary differential equation (NODE). Moreover, the Jacobi elliptic method is used to solve the NODE, where many novel double periodic, kink, and solitary wave solutions are obtained. Additionally, we have chosen to plot periodic, kink, and soliton QDAWs solutions according to some choices for the variable coefficients. According to the a chieved results, we can conclude that the choices of the functional forms of the variable coefficients can control the QDAWs propagation. Finally, the new discovered results may have many important applications in astrophysics, atmospheric science, nanotechnology, and industrial plasma physics.

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Novel solitons and periodic wave solutions for Davey–Stewartson system with variable coefficients

Cited by 18 publications

References 42 publications

New rogon waves for the nonautonomous variable coefficients Schrö dinger equation

New rogon waves for the nonautonomous variable coefficients Schrö dinger equation

Application of DRBEM for 2D sine-Gordon equation

Novel nonlinear quantum dust acoustic waves for modified variable coefficients Zakharove–Kusnetsov equation in dusty plasma

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