New extensions of (2+1)-dimensional BLMP models with soliton solutions

Darvishi, M. T.; Najafi, Mohammad; Arbabi, Somayeh; Rezazadeh, Hadi; Bekir, Ahmet; Çevikel, Adem C.

doi:10.1007/s11082-023-04862-1

Cited by 5 publications

(2 citation statements)

References 52 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the development of NPDE research, a large number of theoretical and application achievements appear constantly, such as the Hirota bilinear approach [1], the long-wave limit technique [2], the inverse scattering approach [3] as well as the Darboux transformation [4], etc. At the same time, Many new solitary waves of NPDE, such as high-breather, kink-shaped soliton, double breathers, high-order lump and high-order rogue wave, attract a lot of attention [5][6][7][8][9][10][11][12]. Unlike soliton with stable structures, lump and breather waves are localized, unstable, and unpredictable in space and can be used to prevent natural disasters.…”

Section: Introductionmentioning

confidence: 99%

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Wang,

Wei,

Huang

2024

Phys. Scr.

View full text Add to dashboard Cite

In this paper, the trajectory equations of 1-lump before and after collision with high-order solitons and the degradation of some novel breather waves are studied in the (2+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation(gCBS). Firstly, we derive N-solitons for the gCBS equation by the Hirota bilinear form. With the help of N-solitons, we obtain M-lump and high-order breather based on the long-wave limit technique and the parametric conjugate method. Secondly, we construct some hybrid waves, such as the hybrid wave between breather and lump. Thirdly, the interaction phenomenon of lump-N-solitonsis investigated, and the theory of its existence is given and proved. Besides, the different degeneracies of double and single breather are discussed. Finally, we also present a large number of two-dimensional and three-dimensional images to better illustrate these nonlinear evolutionary behaviors.

show abstract

Section: Introductionmentioning

confidence: 99%

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Wang,

Wei,

Huang

2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Qi et al obtained the breather molecule, the breather-soliton molecule, some localized interaction solutions and some hybrid solutions of the BLMP equation through a compound method consisting of the velocity resonance, partial module resonance and degeneration of the breather techniques [31]. Considering the simplified Hirota's method and the Cole-Hopf transformation, the authors obtained some new multiple front wave solutions of (2 +1)-dimensional BLMP equation [32]. Moreover, the above-mentioned BLMP equation are generalized to the version with fractional derivatives [33,34], and some interesting traveling wave solutions are generated by the Sardar subequation method.…”

Section: Introductionmentioning

confidence: 99%

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

He,

Han,

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

Based on the Hirota bilinear method, we systematically investigate the (3+1)-dimensional Boiti-Leon-Manana-Pempinelli (BLMP) equation in incompressible fluids and main results include: (1) the formulas of N-kink-soliton solutions and the bound states of multi solitons are all presented, (2) the lump solution is derived by the positive quadratic function method, (3) the interactional solutions are given, i.e., one lump interacts with one- and two-kink-soliton, (4) some special periodic solutions are discussed, i.e., lump-periodic solutions and homoclinic breather solutions.

show abstract

A new analytic approach and its application to new generalized Korteweg‐de Vries and modified Korteweg‐de Vries equations

Kumar,

Malik

2024

Math Methods in App Sciences

View full text Add to dashboard Cite

The current study is important from two perspectives. Firstly, in this article, we suggest a novel analytical technique for creating the exact solutions to nonlinear partial differential equations (NLPDEs). In order to study the dynamical behaviors of various wave phenomena, we can construct the several exact solutions in the form of Jacobi elliptic solutions, hyperbolic solutions, trigonometric solutions, and exponential solutions by using this method. Secondly, we consider a more generalized form of the (2+1)‐dimensional Korteweg–de Vries (KdV) and modified Korteweg‐de Vries (mKdV) equations that plays an important role in describing the shallow water. We successfully extract several soliton solutions for the examined equation. By choosing the appropriate parameters, some graphs of the discovered solutions have been represented in the figures. Every obtained solution has been demonstrated to satisfy the corresponding equation. The findings demonstrate that the method can be applied to solve a number of nonlinear evolution equations. The new solutions and the paper's findings could improve our understanding of how the waves move through shallow water and open up new research avenues.

show abstract

New extensions of (2+1)-dimensional BLMP models with soliton solutions

Cited by 5 publications

References 52 publications

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Evolution of multi-solitons and interaction behaviors of lump to a (2+1) dimensional generalized shallow water wave model

Solitons, lump and interactional solutions of the (3+1)-dimensional BLMP equation in incompressible fluid

A new analytic approach and its application to new generalized Korteweg‐de Vries and modified Korteweg‐de Vries equations

Contact Info

Product

Resources

About