Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

The reflection carried out in this manuscript concerns the construction of prototypes of hybrid solitary waves, solutions of the (2+1)-dimensional complex Ginzburg-Landau equation. The principle of construction consists in injecting into the equation to be solved an ansatz that one would like solution, and that its analytical sequence results from a combination of the analytical sequences of the classical solitary waves. Then, the constraints imposed by the resolution allow to extract exact or approximate solution. As part of this work, the solution function to be constructed from the start is made up of a combination of four analytical sequences of solitary waves of the kink and pulse type. To this end, we have obtained, using a rigorous mathematical approach, important results whose graphic exploitations have made it possible to better characterize them.

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“…(29), ( 30), ( 31), (38), (39) and ( 40) are verified while eqs. ( 32) to (37) as well as (41) to (46) lead to, respectively…”

Section: First Range Of Equations -From the Real Partmentioning

confidence: 99%

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Ngantcha

Omanda²,

Tchaho³

et al. 2022

CJAST

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“…These observations sufficiently show what will be the importance of the impact of the variations of the coefficient c on the formation of the wave structures that we will obtain. By continuing, the insertion of Equation (37) into Equation (20) and Equation (26) gives, successively 37) and (38) in the Equation ( 22) gives, respectively Open Journal of Applied Sciences It is important to emphasize here that, the two conditions which validate Equations ( 39) and ( 42) impose on to take 36), ( 37), ( 38), ( 40) and (41) verify Equation (24). We thus obtain the first family of solutions under the form ; 6 30…”

Section: Analytical Higher Order Solitary Wave Solutionsmentioning

confidence: 99%

Higher Order Solitary Wave Solutions of the Standard KdV Equations

Tchaho¹,

Omanda²,

Mbourou³

et al. 2021

OJAppS

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Considered under their standard form, the fifth-order KdV equations are a sort of reading table on which new prototypes of higher order solitary waves residing there, have been uncovered and revealed to broad daylight. The mathematical tool that made it possible to explore and analyze this equation is the Bogning-Djeumen Tchaho-Kofané method extended to the new implicit Bogning' functions. The analytical form of the solutions chosen in this manuscript is particular in the sense that it contains within its bosom, a package of solitary waves made up of three solitons, especially, the bright type soliton, the hybrid soliton and the dark type soliton which we estimate capable in their interactions of generating new hybrid or multi-form solitons. Existence conditions of the obtained solitons have been determined. It emerges that, these existence conditions of the chosen ansatz could open the way to other new varieties of fifth-order KdV equations including to which it will be one of the solutions. Some of the obtained solitons are exact solutions. Intense numerical simulations highlighted numerical stability and confirmed the hybrid character of the obtained solutions. These results will help to model new nonlinear wave phenomena, in plasma media and in fluid dynamics, especially, on the shallow water surface.

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“…In the past some decades, novel exact solutions may help to find new phenomena. A variety of powerful techniques, such as inverse scattering scheme, [1,2] Hirota bilinear tranformation [3,4], the tanh-sech method [5][6][7][8], sine-cosine method [9,10], Expfunction method [11][12][13][14] and ¢ G G ( ) expansion methods [15][16][17][18][19][20], the Lie group symmetry method [21], the homotopy analysis scheme [22,23], the first integration technique [24],the theta function method [25,26], the homogeneous balance method [27], the Jacobi elliptic function method [28,29], the Adomian decomposition method [30] and Some new and important developments for searching for analytical solitary wave solutions for NLPDEs as [31][32][33][34][35][36][37][38][39][40][41] were used to develop nonlinear dispersive and dissipative nonlinear wave problems.…”

Section: Introductionmentioning

confidence: 99%

Dispersive analytical wave solutions of the strain waves equation in microstructured solids and Lax’ fifth-order dynamical systems

Seadawy¹,

Ali²,

Băleanu³

et al. 2021

Phys. Scr.

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In this manuscript, with the prosperously implementation of two mathematical techniques, several types solitary waves solution of the micro-structured solids wave and the Lax' fifth-order (Lax5) equations are successfully and investigated with the aid of the mathematical software of Mathematica. These schemes namely called ameliorated form of simple equation and modified F-expansion methods. By substituting the diverse values to the parameters, variants wave results are discovered from exact peregrinating wave solution. Some solutions have been exemplified by graphical to understand the physical phenomena of the micro-structured solids wave and the Lax' fifth-order (Lax5) models. The accomplished solutions seem with all essential constraint conditions, which are obligatory for them to subsist. Hence our techniques via fortification of symbolic computations provide an active and potent mathematical implement for solving diverse benevolent nonlinear wave problems.

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Multi-form solitary wave solutions of the KdV-Burgers-Kuramoto equation

Cited by 7 publications

References 34 publications

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Hybridization of Solitary Wave Solutions in (2+1)-dimentional Complex Ginzburg-Landau Equation

Higher Order Solitary Wave Solutions of the Standard KdV Equations

Dispersive analytical wave solutions of the strain waves equation in microstructured solids and Lax’ fifth-order dynamical systems

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