Exact solutions for the Bogoyavlensky-Konopelchenko equation with variable coefficients with an efficient technique

Mohanty, Shruti; Pradhan, Balaram; Sagidullayeva, Zhanna; Myrzakulov, Ratbay; Dev, Apul N.

doi:10.1016/j.aej.2023.04.001

Cited by 4 publications

(1 citation statement)

References 37 publications

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“…The solutions of this reaction-diffusion equation will be used in our study to solve the vcBKdV Equation (1). More precisely, the following solutions of (8) will be used [59]:…”

Section: An Auxiliary Equation Of the Reaction-diffusion Typementioning

confidence: 99%

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

Cimpoiasu,

Constantinescu

2024

Symmetry

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A (2+1)-dimensional fourth order Burgers–KdV equation with variable coefficients (vcBKdV) is studied here and interesting wave-type solutions with variable amplitudes and velocities are reported. The model has been not previously studied in the chosen form and it presents a twofold interest: as a model describing a rich variety of phenomena and as a higher-order equation solving difficulties generated by the presence of the variable coefficients. The novelty of our approach is related to the use of the functional expansion, a solving method based on an auxiliary equation that generalizes other approaches, such as, for example, the G′G proved here. We use a similarity reduction with a nonlinear wave variable that leads to a determining system that it is not usually algebraic, but an over-determined system of partial differential equations. It depends on 14 constant or functional parameters and can generate much richer classes of solutions. Three such classes of solutions, corresponding to the case when a specific form of the generalized reaction–diffusion equation is used as auxiliary equation, are considered. The influence on the dynamical behavior of two important factors, the choices of the auxiliary equation and the form of solution, are studied by providing graphical representations of specific solutions for various values of the parameters.

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“…The solutions of this reaction-diffusion equation will be used in our study to solve the vcBKdV Equation (1). More precisely, the following solutions of (8) will be used [59]:…”

Section: An Auxiliary Equation Of the Reaction-diffusion Typementioning

confidence: 99%

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

Cimpoiasu,

Constantinescu

2024

Symmetry

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An expansion method for generating travelling wave solutions for the (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients

Yokuş,

Duran,

Kaya

2024

Chaos, Solitons & Fractals

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Abundant solitons for the generalized Hirota–Satsuma couple KdV system with an efficient technique

Mohanty

2024

Chinese Journal of Physics

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Exact solutions for the Bogoyavlensky-Konopelchenko equation with variable coefficients with an efficient technique

Cited by 4 publications

References 37 publications

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

Wave Solutions for a (2 + 1)-Dimensional Burgers–KdV Equation with Variable Coefficients via the Functional Expansion Method

An expansion method for generating travelling wave solutions for the (2 + 1)-dimensional Bogoyavlensky-Konopelchenko equation with variable coefficients

Abundant solitons for the generalized Hirota–Satsuma couple KdV system with an efficient technique

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