A construction of new exact periodic wave and solitary wave solutions for the 2D Ginzburg–Landau equation

Achab, Abdelfattah El; Amine, A.

doi:10.1007/s11071-017-3924-0

Cited by 13 publications

(7 citation statements)

References 31 publications

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“…Most standard methods for solving NLEE based on transfer these equations to ODE, using appropriate transformation and then solve it, which give travelling wave solutions and consequently give the solutions of the original NLEE. We observed that there are so many classes of NLEE arising in physics, fluid mechanics and engineering fields transferred to the following ODE: 3 0 αθ βθ γθ ′′ + + = (4) see [9,10,19,[22][23][24][25][26][27][28][29]31] and so on. This equation is often referred to the pseudoptential or sagdeev potential [30].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the cubic Boussinesq and the coupled Higgs system

2020

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We present explicit exact solutions of some evolution equations including cubic Boussinesq and coupled Higgs system by the unified method. The explicit solutions are expressed in terms of some elementary functions including trigonometric, exponential, and polynomial. The method is applied to a number of special test problems to test the strength of the method and computational results indicate the power and efficiency of the method.

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Section: Introductionmentioning

confidence: 99%

Exact solutions of the cubic Boussinesq and the coupled Higgs system

2020

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“…see for example [27][28][29][30][31][32][33][34][35][36][37][38][39]. This observation gives this equation special and important feature.…”

Section: Introductionmentioning

confidence: 86%

Nonlinearity contributions on critical MKP equation

Abdelwahed

2020

Journal of Taibah University for Science

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The mathematical new plasma wave solutions are specified in the compose of trigonometric, rational, hyperbolic, periodic and explosive kinds that are realistic for Modified-Kadomtsev-Petviashvili (MKP) equation. Also, numeral studies for the acquired solutions have been reveals that periodic, shock and explosive new forms may applicable in D-F Earth's ionosphere plasma. The used method is influential and robust in comparison applications in plasma fluids. To depict the propagating soliton profiles in a plasma medium, it is needful to solve MKP equation at a critical mass ratio. The Riccati-Bernoulli sub-ODE technique has been utilized to introduce some new important and applicable solutions. The number of these MKP solutions give a leading deed in applied ion acoustics in ionosphere.

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“…see [3,10,[35][36][37][38][39][40][41][42] and so on. Indeed this equation represents a Hamiltonian system with interesting applications [43].…”

Section: Introductionmentioning

confidence: 99%

A robust and accurate solver for some nonlinear partial differential equations and tow applications

Abdelrahman

Alkhidhr

2020

Phys. Scr.

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In this paper we introduce a robust and accurate solver in order to solve various classes of nonlinear partial differential equations. This solver gives the closed formula for the solutions. Within this respect, a solver is developed to accurately resolve and represent the complete wave structure of the nonlinear partial differential equations. To verify this solver, the two applications are introduced. The obtained solutions may be applicable for some new observations in physics, fluid mechanics, biology, engineering, economy, astrophysics, meteorological topics, gravitational collapse and laser technology. The theoretical study and obtained solutions reported illustrating that the proposed solver efficient and adequate. The shape for the obtained solutions are illustrated via 2D and 3D plots for suitable values of the free parameters.

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A construction of new exact periodic wave and solitary wave solutions for the 2D Ginzburg–Landau equation

Cited by 13 publications

References 31 publications

Exact solutions of the cubic Boussinesq and the coupled Higgs system

Exact solutions of the cubic Boussinesq and the coupled Higgs system

Nonlinearity contributions on critical MKP equation

A robust and accurate solver for some nonlinear partial differential equations and tow applications

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