Pfaffian solutions and extended Pfaffian solutions to (3 + 1)-dimensional Jimbo–Miwa equation

Tang, Yaning

doi:10.1016/j.apm.2013.01.037

Cited by 16 publications

(3 citation statements)

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“…With the development of the nonlinear science, exact solutions for the nonlinear evolution equations (NLEEs) have been of significance for the numerical and experimental investigations [1][2][3]. Accordingly, many methods have been proposed to construct exact solutions, including the Hirota bilinear method [4,5], Darboux transformation [6][7][8][9][10] and Pfaffian technique [11][12][13][14]. Among these methods, the Pfaffian technique has been demonstrated to be useful tools for constructing N-th order exact solutions, because these techniques admit direct verifications of the solutions.…”

Section: Introductionmentioning

confidence: 99%

Pfaffian and extended Pfaffian solutions for a (3+1)-dimensional generalized wave equation

Lan

2019

Phys. Scr.

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Under investigation in this paper is a (3+1)-dimensional generalized wave equation, which is the second equation in the Kadomtsev–Petviashvili hierarchy. Linear partial differential conditions presented in this paper are different from the previous study. Pfaffian and extended Pfaffian solutions with a real function φ(y) have been obtained based on these linear partial differential conditions, where y is the scaled space coordinate, and compared with the solutions obtained in the previous articles, the advantage of our ones is that φ(y) could represent an inhomogeneous medium to influence or control the shape of waves. Specific solutions, namely the first- and second-order exact solutions from the Pfaffian and extended Pfaffian solutions are discussed. Discussions indicate that the first- and second-order exact solutions are of the same shape as the corresponding one- and two-soliton solutions on the x−t or z−t plane but of the different shape on the y−t plane.

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Section: Introductionmentioning

confidence: 99%

Pfaffian and extended Pfaffian solutions for a (3+1)-dimensional generalized wave equation

Lan

2019

Phys. Scr.

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“…(1.1). For example, its exact solutions were explicitly given by transformed rational function method [24], the soliton solutions and Wronskian determinant solutions have been obtained by Hirota bilinear forms and Wronskian technique [25][26][27], the Bäcklund transformations and Lax system were discussed by Bell-polynomials theory [28], the lump and lump-type solutions have been derived by Hirota bilinear method [29][30][31][32][33][34][35][36] and some periodic wave solutions also have been found in Refs. [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

New periodic wave solutions of a (3+1)-dimensional Jimbo–Miwa equation

Zhang¹

2019

SN Appl. Sci.

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A new three-wave method is efficient and well-developed approach to solve nonlinear partial differential equation. In this paper, a (3+1)-dimensional Jimbo-Miwa equation is investigated by using this approach. Some periodic wave solutions and kink solutions are obtained through the Hirota bilinear form. Furthermore, figures of some special periodic wave solutions and kink solutions are presented to illustrate the dynamical features of these solutions.where f = f (x, y, z, t) is also real function with respect to variables x, y, z and t. D 3x D y , D t D y and D x D z are called Hirota bilinear operators [23] defined by Publisher's Note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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“…Multiple-soliton solutions of (1) and its extended version were given in Wazwaz [26]. Tang in [27] obtained its Pfaffian solution and extended Pfaffian solutions with the aid of the Hirota bilinear form. Su et al [28] constructed its Wronskian and Grammian solutions.…”

Section: Introductionmentioning

confidence: 99%