Solitary wave fission and fusion in the (2+1)-dimensional generalized Broer–Kaup system

Dai, Chao-Qing; Liu, Cuiyun

doi:10.15388/na.17.3.14055

Cited by 8 publications

(4 citation statements)

References 20 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Applying the painlevé analysis method, the Painlevé-Bäcklund transformation [43,44] of the (2+1)-dimensional dispersive long wave equation is written as follows…”

Section: Lump Solutionsmentioning

confidence: 99%

Rational solutions and their interaction solutions for the (2+1)-dimensional dispersive long wave equation

Zhang

2020

Phys. Scr.

View full text Add to dashboard Cite

The Hirota bilinear form of the (2+1)-dimensional dispersive long wave equation by the truncated painlevé series in this paper is obtained. Meanwhile, a pair of quartic-linear forms are also constructed by an appropriate selection of seed solution to explore the lump solutions of the (2+1)-dimensional dispersive long wave equation. Then some novel interaction solutions by combining quadratic functions and exponential functions are yielded. Finally, in order to better illustrate the features of the results, we draw the three-dimensional and two-dimensional figures.

show abstract

“…Applying the painlevé analysis method, the Painlevé-Bäcklund transformation [43,44] of the (2+1)-dimensional dispersive long wave equation is written as follows…”

Section: Lump Solutionsmentioning

confidence: 99%

Rational solutions and their interaction solutions for the (2+1)-dimensional dispersive long wave equation

Zhang

2020

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…The investigation of soliton solutions for nonlinear evolutional equations [6,24] is an essential and important issue in nonlinear science. As a ubiquitous and significant nonlinear evolutional model, nonlinear Schrödinger equation (NLSE) appears in various fields of physics and engineering from nonlinear optics [36], plasmas [33], fluid dynamics [25] to Bose-Einstein condensations (BECs) [27].…”

Section: Introductionmentioning

confidence: 99%

Spatiotemporal superposed rogue-wave-like breathers in a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation

Zhu

Chen

2016

NAMC

View full text Add to dashboard Cite

A one-to-one relation between a variable-coefficient (3 + 1)-dimensional nonlinear Schrödinger equation with linear and parabolic potentials and the standard nonlinear Schrödinger equation is presented, and then superposed rogue-wave-like breather solution is obtained. These explicit expressions, describing the evolution of the amplitude, width, center and phase, imply that the diffraction, nonlinearity and gain/loss parameters interplay together to influence evolutional characteristics above. Moreover, the controllable mechanism for fast excitation, maintenance, restraint and recurrence of breather is studied. We also provide an experimental scheme to observe these phenomena in future experiments.

show abstract

“…The investigation of soliton solutions is an essential and important issue in nonlinear science. A vast variety of significant methods have been established such as the F -expansion method [10], the multilinear variable separation approach (MLVSA) [4], the Painlevé method [13], the mapping method [8], and the similarity transform method [5], and the like. Note that Navickas et al [18] have remarked the Exp-function method and Zhao et al [23] have also remarked the (G /G)-expansion method.…”

Section: Introductionmentioning

confidence: 99%

“…Lou et al [12] and Ma et al [15] obtained some variable separation solutions for the special model with a = b, respectively. Zheng et al [4] discussed some semifolded localized coherent structures via MLVSA. Ma et al [14] investigated also complex wave excitations and chaotic patterns for Eq.…”

Section: Introductionmentioning

confidence: 99%

Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures

Dai

Liu

2015

NAMC

Self Cite

View full text Add to dashboard Cite

We analyze the extended tanh-function method to realize variable separation, however, we find that various "different" solutions obtained by this method are seriously equivalent to the general solution derived by the multilinear variable separation approach. In order to illustrate this point, we take a general (2+1)-dimensional Korteweg-de Vries system in water for example. Eight kind of variable separation solutions for a general (2 + 1)-dimensional Korteweg-de Vries system are derived by means of the extended tanh-function method and the improved tanh-function method. By detailed investigation, we find that these seemly independent variable separation solutions actually depend on each other. It is verified that many of so-called "new" solutions are equivalent to one another. Based on the uniform variable separation solution, abundant localized coherent structures can be constructed. However, we must pay our attention to the solution expression of all components to avoid the appearance of some un-physical related and divergent structures: seemly abundant structures for a special component are obtained while the divergence of the corresponding other component for the same equation appears.

show abstract

Solitary wave fission and fusion in the (2+1)-dimensional generalized Broer–Kaup system

Cited by 8 publications

References 20 publications

Rational solutions and their interaction solutions for the (2+1)-dimensional dispersive long wave equation

Rational solutions and their interaction solutions for the (2+1)-dimensional dispersive long wave equation

Spatiotemporal superposed rogue-wave-like breathers in a (3+1)-dimensional variable-coefficient nonlinear Schrödinger equation

Be careful with variable separation solutions via the extended tanh-function method and periodic wave structures

Contact Info

Product

Resources

About