Novel multiple solitons, their bifurcations and high order breathers for the novel extended Vakhnenko–Parkes equation

Du, Shaokun; Haq, Noor Ul; Rahman, Mati Ur

doi:10.1016/j.rinp.2023.107038

Cited by 19 publications

(4 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…where λ i can be obtained from equation (10). Inserting equation (11) in the equation ( 9) one can get the following exact solution:…”

Section: First Order Solitonmentioning

confidence: 99%

“…Soliton breathers, observed in diverse physical systems, exhibit localized waves with quasi-periodic and periodic behavior. This study explores first and second-order breather solutions, providing insights applicable across domains [10]. By applying complex conjugations to parameters in auxiliary functions, these solutions offer valuable insights into nonlinear system behaviors, particularly in fields like nonlinear optics.…”

Section: Breather Wavesmentioning

confidence: 99%

“…Among these, HB method is crucial one and has been used for analyzing more complex dynamics of solitons of integrable systems. The bifurcation and breather solitons of extended Vakhnenko-Parkes equation has been exlpored using HB method [10]. Using HB appraoch, more complex dynamics such as resonance, fission and fusion of higher order solitons, breathers and rouge waves of KdV and Sawada-Kotera equations have been analyzed [11,12].…”

Section: Introduction and Related Workmentioning

confidence: 99%

See 2 more Smart Citations

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Saifullah,

Ahmad,

Ali Khan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

The potential Kadomtsev-Petviashvili (pKP) equation delineates the development of small-amplitude, nonlinear, long waves characterized by a gradual variation in the transverse coordinate. The B-type KP equation outlines the relationships among exponentially localized shapes and was employed as a representation for shallow water waves and plasma physics. In this paper, we consider the combined pKP-BKP integrable equation. We discuss the multiple solitons of a newly proposed (3+1)-dimensional combined pKP-BKP integrable equation. We use the Hirota bilinear (HB) form of the considered equation to deduce fission process in higher order solitons with different orders. Moreover, the breather dynamics and its interaction with other solitons are investigated via HB. The lump solution and its interaction with first order and fourth order kink soliton is studied.

show abstract

“…where λ i can be obtained from equation (10). Inserting equation (11) in the equation ( 9) one can get the following exact solution:…”

Section: First Order Solitonmentioning

confidence: 99%

Section: Breather Wavesmentioning

confidence: 99%

Section: Introduction and Related Workmentioning

confidence: 99%

See 1 more Smart Citation

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Saifullah,

Ahmad,

Ali Khan

et al. 2024

Phys. Scr.

View full text Add to dashboard Cite

show abstract

“…Similarly various integral transforms [25,26] are implemented to solve higher order partial differential equations. Also various new soliton solution approaches are investigated; like Sardar sub-equation technique [27], multi soliton solution of Vakhnenko-Parkes equation [28], Coke price prediction approach [29], multivariate stochastic volatility models by using optimization mechanisms [30], Galilean transformation of Schrodinger equation [31], bifurcation analysis of Hindmarsh-Rose model [32] etc B-spline collocation [33][34][35] and the block method [36,37] are additional techniques that improve the current article and are advantageous to the existing system.…”

Section: Introductionmentioning

confidence: 99%

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Sahu,

Jena

2024

Phys. Scr.

View full text Add to dashboard Cite

An essential aspect of mathematical physics is the PHI-four equation, which is a specific version of the Klein-Gordon equation that predicts particle physics phenomena. The present paper addresses numerical approaches to generalized PHI-four equation based on Laplace Adomian Decomposition Technique (LADT) which is governed by coupling of Laplace transform and Adomian decomposition method to determine the kink-antikink single waves in dispersion systems arises in mathematical physics. The nonlinear terms in the PHI-four equation are handled using the accelerated polynomial i.e., Adomian polynomial. The approach is extremely interesting computationally and is straightforward to execute. The accuracy and robustness of the current scheme are demonstrated by four test problems. To demonstrate the efficacy of our suggested approach, the current result is contrasted with both the analytical solution and existing solutions in literature. Stability and convergence analysis are well developed to justify the applicability of the current approach.

show abstract

Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative

Alzahrani,

Saadeh,

Abdoon

et al. 2024

J Eng Math

View full text Add to dashboard Cite

Novel multiple solitons, their bifurcations and high order breathers for the novel extended Vakhnenko–Parkes equation

Cited by 19 publications

References 41 publications

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

Multiple solitons with fission and multi waves interaction solutions of a (3+1)-dimensional combined pKP-BKP integrable equation

The kink-antikink single waves in dispersion systems by generalized PHI-four equation in mathematical physics

Effective methods for numerical analysis of the simplest chaotic circuit model with Atangana–Baleanu Caputo fractional derivative

Contact Info

Product

Resources

About