Dynamics of rational solutions in a new generalized Kadomtsev–Petviashvili equation

The main goal of this paper is to present a new approximate analytical method called modified generalized Taylor fractional series method (MGTFSM) for solving general nonlinear time-fractional partial differential equations. The fractional derivative is considered in the Caputo sense. We establish the convergence results of the proposed method. The basic idea of the MGTFSM is to construct the solution in the form of infinite series which converges rapidly to the exact solution of the given problem. The main advantage of the proposed method compare to current methods is that method solves the nonlinear problems without using linearization, discretization, perturbation or any other restriction. The efficiency and accuracy of the MGTFSM is tested by means of different numerical examples. The results prove that the proposed method is very effective and simple for solving the nonlinear time-fractional partial differential equations problems.

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“…So, the theory of NFPDEs is a powerful theory to give a solution to engineering problems. See for example [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15].…”

Section: Introductionmentioning

confidence: 99%

A new approximate analytical method and its convergence for nonlinear time-fractional partial differential equations

Khalouta

Kadem

2021

Scientia Iranica

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“…There are different rational wave solutions to differential equations; for example, multiple soliton solutions, breather solutions, rogue solutions, and so on. During the last decades, many effective methods such as inverse scattering method [4], Hirota's direct method [11], multiple exp-function method [1,15,21,22], simplified Hirota's method [9,10,12,27,28,[30][31][32][33], and ansatz methods [2,13,25,26,29] have been exerted to find rational wave solutions of differential equations. More articles can be found in [3, 5-8, 16-19, 23, 24, 34, 35].…”

Section: Introductionmentioning

confidence: 99%

Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

Hosseini

Mirzazadeh

Aligoli

et al. 2020

Math. Model. Nat. Phenom.

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A generalized form of (2+1)-dimensional Hirota bilinear (2D-HB) equation is considered herein in order to study nonlinear waves in fluids and oceans. The present goal is carried out through adopting the simplified Hirota’s method as well as ansatz approaches to retrieve a bunch of rational wave structures from multiple soliton solutions to breather, rogue, and complexiton solutions. Some figures corresponding to a series of rational wave structures are provided, illustrating attractive physical behaviors. Results of the current study reveal that the generalized 2D-HB equation is completely integrable and therefore guaranties the existence of multiple soliton solutions of any order.

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“…The Kadomtsev-Petviashvili-type equations have been introduced to describe the water waves in long wavelengths with the weakly nonlinear restoring forces, waves in the ferromagnetic media and matter waves in the Bose-Einstein condensates [1][2][3][4][5][6][7][8][9][10][11][12], and have been applied to investigate the motion of the near-resonant wave humps in the near shore of Harilaid [13], long and rouge waves in the river Seven Ghosts [14], dynamics of the tsunamis generated by undersea earthquakes in the northern Indian Sea [15], and interaction/generation of the longcrested internal solitary waves in the South China Sea [16]. Methods to solve such equations have been proposed, including the Darboux transformation [17][18][19][20][21][22][23][24][25][26][27][28][29], Bäcklund transformation [30,31], Hirota bilinear method [32][33][34][35][36], inverse scattering method [37][38][39], multiple exp-function method [40][41][42][43], similarity transformation…”

Section: Introductionmentioning

confidence: 99%

Solitons and periodic waves for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

Wang

Gao

Ding

et al. 2020

Commun. Theor. Phys.

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Under investigation in this paper is a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics. Soliton and one-periodic-wave solutions are obtained via the Hirota bilinear method and Hirota–Riemann method. Magnitude and velocity of the one soliton are derived. Graphs are presented to discuss the solitons and one-periodic waves: the coefficients in the equation can determine the velocity components of the one soliton, but cannot alter the soliton magnitude; the interaction between the two solitons is elastic; the coefficients in the equation can influence the periods and velocities of the periodic waves. Relation between the one-soliton solution and one-periodic wave solution is investigated.

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Dynamics of rational solutions in a new generalized Kadomtsev–Petviashvili equation

Cited by 45 publications

References 21 publications

A new approximate analytical method and its convergence for nonlinear time-fractional partial differential equations

A new approximate analytical method and its convergence for nonlinear time-fractional partial differential equations

Rational wave solutions to a generalized (2+1)-dimensional Hirota bilinear equation

Solitons and periodic waves for a generalized (3+1)-dimensional Kadomtsev–Petviashvili equation in fluid dynamics and plasma physics

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