On solitary wave solutions for the extended nonlinear Schrödinger equation via the modified F-expansion method

Özişik, M.N.; Seçer, Aydın; Bayram, Mustafa

doi:10.1007/s11082-022-04476-z

Cited by 50 publications

(13 citation statements)

References 61 publications

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“…where k and l are the latitudinal and longitudinal wavenumbers of ocean internal solitary waves, respectively, and c represents the frequency of ocean internal solitary waves. Substituting equation (51) into equation (50) yields Integrating once over equation (52) gives…”

Section: The Solitary Solutions Of Fifth-order Mkp Equations and Anal...mentioning

confidence: 99%

“…Zha et al [49,50], by the Darboux transformation method, investigated Rogue waves arising on the background of two families of periodic standing waves in the Kadomtsev-Petviashvili I (KP-I) equation. Ozisik et al [51,52], by using the F-expansion method, obtained the soliton solution of Kadomtsev-Petviashvili equation. Mia et al [53,54] by using the ¢ G G expansion method to find the novel exact travelling wave solutions of the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona-Mahony (KP-BBM) equation.…”

Section: Introductionmentioning

confidence: 99%

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A novel model for the fifth-order mKP equation describing (2+1)-dimensional shallow ocean solitary waves and their properties

Zhao,

Gao,

Yang

et al. 2023

Phys. Scr.

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In this paper, we develop a (2+1)-dimensional fifth-order modified Kadomtsev-Petviashvili (mKP) equation model using multiscale analysis and perturbation expansion, which is a novel model description of the shallow ocean solitary waves phenomenon, featuring stronger nonlinear terms and a higher-order compared to traditional models. We examine the conservation law within the model to further investigate the properties of solitary waves. Subsequently, we obtain the exact solutions of the model by employing the G'/G expansion method. We simulate the generation and propagation of solitary waves through appropriate parameter adjustments, deriving the solitary wave solutions, kink wave solutions, and periodic wave solutions. Additionally, we analyze the effects of different parameters on the propagation of solitary waves. Finally, we explore the evolution of solitary waves before and after generation under a given initial condition. This study contributes to a deeper understanding of the intricate dynamics of shallow ocean solitary waves, shedding light on their behaviour and implications.

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Section: The Solitary Solutions Of Fifth-order Mkp Equations and Anal...mentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

A novel model for the fifth-order mKP equation describing (2+1)-dimensional shallow ocean solitary waves and their properties

Zhao,

Gao,

Yang

et al. 2023

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Various researchers have introduced numerous analytical approaches to attain solitary waves solutions. Some of them are listed in [4][5][6][7][8][9]. Among these, HB method is crucial one and has been used for analyzing more complex dynamics of solitons of integrable systems.…”

Section: Introduction and Related Workmentioning

confidence: 99%

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Saifullah,

Ahmad,

Ali Khan

et al. 2024

Phys. Scr.

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The potential Kadomtsev-Petviashvili (pKP) equation delineates the development of small-amplitude, nonlinear, long waves characterized by a gradual variation in the transverse coordinate. The B-type KP equation outlines the relationships among exponentially localized shapes and was employed as a representation for shallow water waves and plasma physics. In this paper, we consider the combined pKP-BKP integrable equation. We discuss the multiple solitons of a newly proposed (3+1)-dimensional combined pKP-BKP integrable equation. We use the Hirota bilinear (HB) form of the considered equation to deduce fission process in higher order solitons with different orders. Moreover, the breather dynamics and its interaction with other solitons are investigated via HB. The lump solution and its interaction with first order and fourth order kink soliton is studied.

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“…To date, extensive research has been carried out on the complex nonlinear waves of KdV equations. Many methods have been developed to solve these equations, such as inverse scattering transformation [1], Darboux-Bäcklund transformation [2,3], Hirota's bilinear method [4,5], the first integral method [6], the homogeneous balance principle [7,8], the F-expansion method [9][10][11], the Wronskian method [12], the variational method [13], and Painlevé analysis [14]. On the other hand, KdV equations have different forms in different models, and the relevant methods were developed to study different types of KdV equations.…”

Section: Introductionmentioning

confidence: 99%

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

Zeng

Liang

et al. 2023

Symmetry

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The exact traveling wave solutions to coupled KdV equations with variable coefficients are obtained via the use of quadratic Jacobi’s elliptic function expansion. The presented coupled KdV equations have a more general form than those studied in the literature. Nine couples of quadratic Jacobi’s elliptic function solutions are found. Each couple of traveling wave solutions is symmetric in mathematical form. In the limit cases m→1, these periodic solutions degenerate as the corresponding soliton solutions. After the simple parameter substitution, the trigonometric function solutions are also obtained.

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On solitary wave solutions for the extended nonlinear Schrödinger equation via the modified F-expansion method

Cited by 50 publications

References 61 publications

A novel model for the fifth-order mKP equation describing (2+1)-dimensional shallow ocean solitary waves and their properties

A novel model for the fifth-order mKP equation describing (2+1)-dimensional shallow ocean solitary waves and their properties

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Exact Solutions for Coupled Variable Coefficient KdV Equation via Quadratic Jacobi’s Elliptic Function Expansion

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