A new implementation of a novel analytical method for finding the analytical solutions of the (2+1)-dimensional KP-BBM equation

Mia, Rajib; Miah, M. Mamun; Osman, M. S.

doi:10.1016/j.heliyon.2023.e15690

Cited by 25 publications

(9 citation statements)

References 46 publications

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“…According to equation equation (55) we have We substitute equation (56) into equation (53) and collect all terms with the same power of ¢ G G . By equating the coefficients of this polynomial in ¢ G G to zero, Calculating the above system of equations by MAPLE yields the following two solutions.…”

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

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%

“…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%

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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“…Kumar et al [ 24 ] have constructed the abundant exact solutions of Eq ( 1.1 ) by using two powerful techniques via the Lie symmetry and the GERF methods. Mia et al [ 25 ] have inspected the novel exact travelling waves solutions of Eq ( 1.1 ) through the ( G ′/ G ′+ G + A )-expansion technique. Tariq and Seadawy [ 26 ] have inspected the analytical soliton solutions by the auxiliary equation method.…”

Section: Introductionmentioning

confidence: 99%

Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis

Rayhanul Islam,

Khan

2024

PLoS ONE

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In this paper, we investigate the (2+1)-dimensional Kadomtsev-Petviashvili-Benjamin-Bona Mahony equation using two effective methods: the unified scheme and the advanced auxiliary equation scheme, aiming to derive precise wave solutions. These solutions are expressed as combinations of trigonometric, rational, hyperbolic, and exponential functions. Visual representations, including three-dimensional (3D) and two-dimensional (2D) combined charts, are provided for some of these solutions. The influence of the nonlinear parameter p on the wave type is thoroughly examined through diverse figures, illustrating the profound impact of nonlinearity. Additionally, we briefly investigate the Hamiltonian function and the stability of the model using a planar dynamical system approach. This involves examining trajectories, isoclines, and nullclines to illustrate stable solution paths for the wave variables. Numerical results demonstrate that these methods are reliable, straightforward, and potent tools for analyzing various nonlinear evolution equations found in physics, applied mathematics, and engineering.

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“…The study of the soliton solutions explores a theoretical reference for the research of nonlinear physical models, soliton control, optical switching equipment and so on. Up to now, many effective and powerful methods have been obtained for constructing the soliton solutions of the NLPDEs, such as the soliton ansatz method [5,6], the Kudryashov method [7], the Hirota's bilinear transform method [8,9], the Darboux transformation method [10,11], the extended trial equation method [12], the Lie symmetry method [13,14], the improved F-expansion approach [15], the invariant subspace method [16,17], the extended sinh-Gordon equation expansion method [18] and the new extended auxiliary equation method [19,20], the G G ¢ ( )-expansion method [21][22][23], the Expfunction method [24,25], the modified simplest equation method [26,27], the decomposition method [28,29], and so on.…”

Section: Introductionmentioning

confidence: 99%

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

Mathanaranjan

Hashemi

Rezazadeh³

et al. 2023

Commun. Theor. Phys.

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The present paper aims to investigate the chirped optical soliton solutions of nonlinear Schr¨odinger equation with nonlinear chromatic dispersion and quadratic-cubic law of refractive index. The exquisite balance between the chromatic dispersion and the nonlinearityassociated with the refractive index of a fiber gives rise to optical solitons, which can travel down the fiber for intercontinental distances. The effective technique, namely, the new extended auxiliary equation method is implemented as a solution method. Different types ofchirped soliton solutions including dark, bright, singular and periodic soliton solutions are extracted from the Jacobi elliptic function solutions when the modulus of the Jacobi elliptic function approaches to one or zero. These obtained chirped optical soliton solutions might play an important role in optical communication links and optical signal processing systems. The stability of the system is examined in the framework of modulational instability analysis.

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A new implementation of a novel analytical method for finding the analytical solutions of the (2+1)-dimensional KP-BBM equation

Cited by 25 publications

References 46 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

Investigating wave solutions and impact of nonlinearity: Comprehensive study of the KP-BBM model with bifurcation analysis

Chirped optical solitons and stability analysis of the nonlinear Schrödinger equation with nonlinear chromatic dispersion

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