Abundant wave solutions to two novel KP-like equations using an effective integration method

Ghanbari, Behzad; Kuo, Chun-Ku

doi:10.1088/1402-4896/abde5a

Cited by 25 publications

(3 citation statements)

References 38 publications

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“…In 2018, an integration method called the generalized exponential rational function method (GERFM) was introduced by Ghanbari et al to solve the resonance nonlinear Schrödinger equation [66]. Following their work, the technique has been used successfully many times to handle other partial equations [67][68][69][70][71][72][73][74][75][76][77][78][79][80][81][82]. In this part, we outline the main steps of GERFM as follows.…”

Section: The Generalized Exponential Rational Function Methodsmentioning

confidence: 99%

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Neirameh

Parvaneh

2021

Adv Differ Equ

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Exact solutions to nonlinear differential equations play an undeniable role in various branches of science. These solutions are often used as reliable tools in describing the various quantitative and qualitative features of nonlinear phenomena observed in many fields of mathematical physics and nonlinear sciences. In this paper, the generalized exponential rational function method and the extended sinh-Gordon equation expansion method are applied to obtain approximate analytical solutions to the space-time conformable coupled Cahn–Allen equation, the space-time conformable coupled Burgers equation, and the space-time conformable Fokas equation. Novel approximate exact solutions are obtained. The conformable derivative is considered to obtain the approximate analytical solutions under constraint conditions. Numerical simulations obtained by the proposed methods indicate that the approaches are very effective. Both techniques employed in this paper have the potential to be used in solving other models in mathematics and physics.

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Section: The Generalized Exponential Rational Function Methodsmentioning

confidence: 99%

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Neirameh

Parvaneh

2021

Adv Differ Equ

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“…In this section, we state the main steps of GERFM as follows (Biazar and Ghanbari 2012 ; Ghanbari and Kuo 2021 ; Kumar et al. 2021 ; Ghanbari and Akgül 2020 ; Ismael et al.…”

Section: Overview Of the Generalized Exponential Rational Function Me...mentioning

confidence: 99%

Investigation of optical solitons to the nonlinear complex Kundu–Eckhaus and Zakharov–Kuznetsov–Benjamin–Bona–Mahony equations in conformable

Baskonus

Gao

2022

Opt Quant Electron

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This research manuscript focuses on the extraction of dark-bright solitons and periodic wave distributions of two models, namely, the Zakharov–Kuznetsov–Benjamin–Bona–Mahony equation and complex Kundu–Eckhaus equation with conformable derivative. To reach these important properties, the generalized exponential rational function method is considered. To observe wave distributions in periodic and singular sense, dynamical behaviour modulus of solutions are also archived. Strain conditions for validity of results obtained in this paper are also reported.

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“…[28][29][30][31][32][33][34][35][36][37][38][39]. Recent methods dealing with NLEEs are generalized exponential rational function method [40], ameliorated form of a modified F-expansion method [41], Φ 6 − model expansion method [42] and the super thermal index method [43].…”

Section: Introductionmentioning

confidence: 99%

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

Elbrolosy

2021

Phys. Scr.

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This work is interested in constructing new traveling wave solutions for the coupled nonlinear Schrödinger type equations. It is shown that the equations can be converted to a conservative Hamiltonian traveling wave system. By using the bifurcation theory and Qualitative analysis, we assign the permitted intervals of real propagation. The conserved quantity is utilized to construct sixteen traveling wave solutions; four periodic, two kink, and ten singular solutions. The periodic and kink solutions are analyzed numerically considering the affect of varying each parameter keeping the others fixed. The degeneracy of the solutions discussed through the transmission of the orbits illustrates the consistency of the solutions. The 3D and 2D graphical representations for solutions are presented. Finally, we investigate numerically the quasi-periodic behavior for the perturbed system after inserting a periodic term.

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Abundant wave solutions to two novel KP-like equations using an effective integration method

Cited by 25 publications

References 38 publications

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Analytical solitons for the space-time conformable differential equations using two efficient techniques

Investigation of optical solitons to the nonlinear complex Kundu–Eckhaus and Zakharov–Kuznetsov–Benjamin–Bona–Mahony equations in conformable

Qualitative analysis and new soliton solutions for the coupled nonlinear Schrödinger type equations

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