Integrability, breather, lump and quasi-periodic waves of non-autonomous Kadomtsev–Petviashvili equation based on Bell-polynomial approach

Raut, Santanu; Barman, Ranjan; Sarkar, Tanay

doi:10.1016/j.wavemoti.2023.103125

Cited by 25 publications

(3 citation statements)

References 72 publications

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“…The Hirota bilinear forms and the generalized bilinear forms are the starting points exhibiting a great convenience in determining lump waves. Interaction solutions between lump waves and other interesting waves, including homoclinic and heteroclinic solutions, can be explored for integrable and nonintegrable model equations (see, e.g., [43][44][45][46][47][48]). Connections with other solution approaches in soliton theory should deserve further investigation, which include Darboux transformations [49,50], the Wronskian technique [51], auto-Bäcklund transformations [52,53], the Riemann-Hilbert technique [54][55][56], symmetry reductions [57,58] and symmetry constraints [59].…”

Section: Discussionmentioning

confidence: 99%

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

2023

Mathematics

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This paper aims to search for lump waves in a spatial symmetric (2+1)-dimensional dispersive wave model. Through an ansatz on positive quadratic functions, we conduct symbolic computations with Maple to generate lump waves for the proposed nonlinear model. A line of critical points of the lump waves is computed, whose two spatial coordinates travel at constant speeds. The corresponding maximum and minimum values are evaluated in terms of the wave numbers, and interestingly, all those extreme values do not change with time, either. The last section is the conclusion.

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Section: Discussionmentioning

confidence: 99%

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

2023

Mathematics

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“…Interparticle collision in general is an common phenomenon in different physical environments. Naturally, damping rises in almost all real-world situations [28]- [35]. Also, there are so many physical situations where external excitation feels, for instance, plasma wave propagating in astronomical space environment moves under the influence of external periodic and hyperbolic forces in many cases [36]- [38].…”

Section: Introductionmentioning

confidence: 99%

“…Especially, Hirota's approach is a popular, efficient, and effective technique to find different complicated solutions of nonlinear partial differential equations viz., multi-soliton, breather, lump, rouge, and positon, etc. [35,38,58]. There are also many other techniques for deriving multisolitons.…”

Section: Introductionmentioning

confidence: 99%

The non-autonomous generalized perturbed KdV equation: its integrability, infinite conservation laws, multi soliton, high-order breather and hybrid solutions with mixed backgrounds

Raut,

Kairi,

Chatterjee

et al. 2023

Preprint

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This paper claims the integrability of the non-autonomous generalized perturbed KdV (NgPKdV) equation through Painlevé analysis. Additionally, bilinear Bäcklund transformations, Lax pairs, and infinite conservation laws are developed to demonstrate the integrability of the said equation. Employing Hirota's approach, multi-solitons of the NgPKdV equation are constructed, from which the breather and hybrid solutions are explored with the proper choice of polynomial functions in the solution space. The changes in the behavior of non-autonomous solitons under different physical conditions are studied with special care. The propagating properties of single and double non-autonomous breathers along with their interactive properties with solitons are observed from the numerical viewpoint. An extensive study is also conducted on the propagation of solitary interactions and complex hybrid solutions. PACS 52.30-q · 94.30.cq · 52.35.Fp

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Existence of periodic wave of a BBM equation with delayed convection and weak diffusion

Wei

2023

Nonlinear Dyn

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This paper focus on the existence and uniqueness of periodic waves for a BBM equation with local strong generic delay convection and weak diffusion. By analyzing the corresponding Hamiltonian system, we aim to obtain the existence of periodic orbit by constructing a locally invariant manifold according to geometric singular perturbation theory. Chebyshev criteria is applied to investigate the ratio of Abelian integrals. We prove the existence and uniqueness of periodic wave solution with sufficiently small perturbation parameter. Moreover, the upper and lower bounds of the limiting wave speed are given. Keywordsdelayed BBM equation • geometric singular perturbation theory • periodic wave • Abelian integrals Mathematics Subject Classification (2020) 34C25 • 34C60 • 37C27 1 IntroductionTraveling wave solutions plays an important role in many mathematically modelled phenomena. It can be applied in comparison principles and characterize the long-term behaviour in numerous situations in conformance with

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Integrability, breather, lump and quasi-periodic waves of non-autonomous Kadomtsev–Petviashvili equation based on Bell-polynomial approach

Cited by 25 publications

References 72 publications

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

Lump Waves in a Spatial Symmetric Nonlinear Dispersive Wave Model in (2+1)-Dimensions

The non-autonomous generalized perturbed KdV equation: its integrability, infinite conservation laws, multi soliton, high-order breather and hybrid solutions with mixed backgrounds

Existence of periodic wave of a BBM equation with delayed convection and weak diffusion

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