Bilinear representations and lump-type waves for a fifth-order nonlinear wave equation

Zhou, Yuefeng; Wang, Chuanjian; Zhang, Xingyong; Fang, Hui

doi:10.1140/epjp/i2019-13083-3

Cited by 6 publications

(4 citation statements)

References 28 publications

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“…As a special localized solution, lump solution is a rational solution decaying in all directions of space and was first discovered by Manakov [14]. Different methods have been applied to investigate lump solutions, such as the inverse scattering transformation [15,16], the Hirota bilinear method [17][18][19][20][21][22], Bäcklund transformation [23][24][25], Darboux transformation method [26,27], and so on. By applying these methods, the lump solutions and the interaction solutions of many nonlinear evolution equations were studied [28][29][30][31].…”

Section: Introductionmentioning

confidence: 99%

Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

Tang

Liang

2021

Phys. Scr.

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In this paper, the Hirota bilinear method is applied to investigate the exact solutions of the (3+1)-dimensional Jimbo-Miwa (JM) equation, including solitons, breathers and lumps, which satisfy specific Wronskian conditions. Their dynamic behaviors and the effects of free parameters on the propagation direction and velocity are analyzed through three-dimensional images and the corresponding contour plots. Especially, based on the 2Mth-order Wronskian determinant solutions, the determinant expression of arbitrary Mth-order lump solutions is constructed by employing elementary transformation and long wave limit. The experimental results show that the interaction between multiple lumps is a completely elastic collision. These results may be helpful to understand the propagation processes of nonlinear waves in some nonlinear physical systems, such as fluid mechanics, nonlinear optics and so on.

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Section: Introductionmentioning

confidence: 99%

Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

Tang

Liang

2021

Phys. Scr.

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“…Based on the above, our motive in this work is to bring light on the rogue wave solutions and their dynamical characteristics for the considered equation (2), since, nowadays, theoretical analysis of such waves has become an integral segment of the field nonlinear sciences. The Hirota bilinear method [44][45][46][47] is found successful in investigating various nonlinear evolution equations to obtain rogue wave solutions and especially it was adopted for low order rogue wave solutions in these studies. Despite the high difficulty level in exploring multiple rogue waves, still, there are few works of literature on it.…”

Section: Introductionmentioning

confidence: 99%

Dynamics of higher-order bright and dark rogue waves in a new (2+1)-dimensional integrable Boussinesq model

et al. 2020

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This work deals with the dynamics of higher-order rogue waves in a new integrable (2+1)-dimensional Boussinesq equation governing the evolution of high and steep gravity water waves. To achieve this objective, we construct rogue wave solutions by employing Bell polynomial and Hirota’s bilinearization method, along with the generalized polynomial function. Through the obtained rogue wave solutions, we explore the impact of various system and solution parameters in their dynamics. Primarily, these parameters determine the characteristics of rogue waves, including the identification of their type, bright or dark type doubly-localized rogue wave structures and spatially localized rational solitons, and manipulation of their amplitude, depth, and width. Reported results will be encouraging to the studies on the rogue waves in higher dimensional systems as well as to experimental investigations on the controlling mechanism of rogue waves in optical systems, atomic condensates, and deep water oceanic waves.

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“…Some properties about lump-type wave solution are demonstrated in virtue of the theoretical analysis and graphical representation. In addition, many researchers have also investigated the interaction between lump-type wave and other type of solitary wave solutions, and some interesting interaction phenomena have been shown [16][17][18][19][20][21][22][23][24].…”

Section: Introductionmentioning

confidence: 99%

“…If we neglect u yyy , then it can be reduced to the Bogoyavlenskii-Schi equation [1]. rough the following transformation [23]:…”

Section: Introductionmentioning

confidence: 99%

Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

Wang

Fang

2020

Complexity

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Lump-type wave solution of the Bogoyavlenskii–Kadomtsev–Petviashvili equation is constructed by using the bilinear structure and Hermitian quadratic form. The dynamical behaviors of lump-type wave solution are investigated and presented analytically and graphically. Furthermore, we discuss the interaction between a lump-type wave and a kink wave solution. Absorb-emit interaction between two kinds of solitary wave solutions is shown. This kind of interaction solution can be regarded as a lump-type wave which propagates on the kink wave background.

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Bilinear representations and lump-type waves for a fifth-order nonlinear wave equation

Cited by 6 publications

References 28 publications

Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

Exact solutions of the (3+1)-dimensional Jimbo-Miwa equation via Wronskian solutions: Soliton, breather, and multiple lump solutions

Dynamics of higher-order bright and dark rogue waves in a new (2+1)-dimensional integrable Boussinesq model

Lump-Type Wave and Interaction Solutions of the Bogoyavlenskii–Kadomtsev–Petviashvili Equation

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