Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

Wu, Jian-Wen; Cai, Yue-Jin; Lin, Ji

doi:10.1088/1674-1056/ac1f08

Cited by 7 publications

(4 citation statements)

References 60 publications

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“…The Painlevé analysis method is an effective way of judging the integrability of nonlinear differential equations and finding exact solutions. [29,30] We now perform the Painlevé analysis on Eq. ( 4) to find integrability conditions.…”

Section: Introductionmentioning

confidence: 99%

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

2023

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This article investigates the Hirota-Satsuma-Ito equation with variable coefficient using the Hirota bilinear method and the long wave limit method. The equation is proved to be Painlevé integrable by Painlevé analysis. On the basis of the bilinear form, the forms of two-soliton solutions, three-soliton solutions and four-soliton solutions are studied specifically. The appropriate parameter values are chosen and the corresponding figures are presented. The breather waves solutions, lump solutions, periodic solutions and the interaction of breather waves solutions and soliton solutions, etc are given in this article. In addition, we also analysed the different effects of the parameters on the figures. The figures of the same set of parameters in different planes are presented to describe the dynamical behaviour of solutions. These are important for describing water waves in nature.

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Section: Introductionmentioning

confidence: 99%

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

2023

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“…The symmetry method is an efficient and universal method for constructing Bäcklund transformations and analytical solutions of nonlinear systems [1][2][3][4][5][6][7][8][9][10]. At the same time, the analytical solutions can describe some nonlinear phenomena and reveal some deep-seated internal relations in nonlinear systems [11][12][13][14][15][16][17][18].…”

Section: Introductionmentioning

confidence: 99%

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Cui

2023

Phys. Scr.

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The $(n+1)$-dimensional generalized KdV equation is presented in this paper, and we further investigate its nonlocal symmetries by different methods. It can be seen that the symmetrical transformations obtained by different nonlocal symmetries are usually equivalent. Based on the obtained Lie point symmetry as well as the $m$th finite symmetrical transformations, we obtain its soliton molecules and multiple soliton solutions. Additionally, for the case of $n=4$ various types of interaction solutions among solitons and periodic waves are obtained by the similarity reduction method.

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“…Recently, Lou discovered that, starting from the non-local symmetries of non-linear equations, the interactions, such as the soliton-Painlevé wave, soliton-cnoidal periodic wave, soliton-KdV wave, etc., can be established [1][2][3][4][5][6]. Moreover, recent researches have also shown that the interaction solutions between solitons and other non-linear excitations can also be obtained by the consistent tanh expansion (CTE) method, which is evolved from the classical tanh function expansion method [7][8][9].…”

Section: Introductionmentioning

confidence: 99%

Non-local residual symmetry and soliton-cnoidal periodic wave interaction solutions of the KdV6 equation

et al. 2023

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The residual symmetry of the KdV6 equation is obtained by the Painlevé truncate expansion. Since the residual symmetry is non-local, five field quantities are introduced to localize it into the local one. Besides, the interaction solutions between solitons and cnoidal periodic waves of the KdV6 equation are constructed by making use of the consistent tanh expansion method. As an illustration, a specific interaction solution in the form of tanh function and Jacobian elliptic function is discussed both analytically and graphically.

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Residual symmetries, consistent-Riccati-expansion integrability, and interaction solutions of a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation

Cited by 7 publications

References 60 publications

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

Interaction solutions and localized waves to the (2+1)-dimensional Hirota–Satsuma–Ito equation with variable coefficient

Nonlocal symmetries and interaction solutions for the (n + 1)-dimensional generalized Korteweg–de Vries equation

Non-local residual symmetry and soliton-cnoidal periodic wave interaction solutions of the KdV6 equation

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