Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves

Mohan, Brij; Kumar, Sachin; Kumar, Raj

doi:10.1007/s11071-023-08938-1

Cited by 28 publications

(2 citation statements)

References 46 publications

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“…In the main study [21], the authors presented the Painlevé integrability analysis of the model. Additionally, they can acquire the rogue waves up to the third order by using computation and the Cole-Hopf transformation.…”

Section: Discussionmentioning

confidence: 99%

New Conformable P-Type $(3+1)$-Dimensional Evolution Equation and its Analytical and Numerical Solutions

Şenol,

Erol

2024

Journal of New Theory

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The paper examines the conformable nonlinear evolution equation in $(3+1)$-dimensions. First, basic definitions and characteristics for the conformable derivative are given. Then, the modified extended tanh-function and $\exp(–\phi(\xi))$-expansion techniques are utilized to determine the exact solutions to this problem. The consequences of some of the acquired data's physical 3D and 2D contour surfaces are used to demonstrate the findings, providing insight into how geometric patterns are physically interpreted. These solutions help illustrate how the studied model and other nonlinear representations in physical sciences might be used in real-world scenarios. It is clear that these methods have the capacity to solve a large number of fractional differential equations with beneficial outcomes.

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Section: Discussionmentioning

confidence: 99%

New Conformable P-Type $(3+1)$-Dimensional Evolution Equation and its Analytical and Numerical Solutions

Şenol,

Erol

2024

Journal of New Theory

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“…Solitons, in particular, are significant in long-distance, high-capacity, and fiber-optic communication systems, because they sustain steady waveform and velocity propagation under the equilibrium of group-velocity dispersion and nonlinear effects [5,6]. In nonlinear science, the soliton theory plays a significant role [7]. The development of soliton theory has become a major tool for solving nonlinear partial differential equations, opening up new directions in the study of nonlinear science.…”

Section: Introductionmentioning

confidence: 99%

Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations

Chen,

Wang,

Yang

et al. 2024

Preprint

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Under investigation in this paper is the coupled modified Korteweg-de Vries equations. Based on Lax pair and Darboux transformation, various vector localized wave solutions are derived and analyzed. We notice that the localized waves have different dynamical behaviors in several components, for example, the bell-shaped soliton and flat-top soliton, or the bell-shaped soliton and two-peak soli-ton, are obtained in two components, respectively. Furthermore, the interactions between two solitons are different in distinct components. In addition, the vector breather and rogue wave solutions are constructed. Especially, the various structures of first-order rogue waves are observed, such as the two-peak rogue waves and flat-top rogue wave, or the dark rogue waves and bright rogue waves. Finally , the vector second-order rogue wave solutions are derived and the strong or weak interaction patterns of second-order rogue waves are achieved.

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Analyzing specific waves and various dynamics of multi-peakons in (3+1)-dimensional p-type equation using a newly created methodology

Dhiman,

Kumar

2024

Nonlinear Dyn

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Higher-order rogue waves and dispersive solitons of a novel P-type (3+1)-D evolution equation in soliton theory and nonlinear waves

Cited by 28 publications

References 46 publications

New Conformable P-Type $(3+1)$-Dimensional Evolution Equation and its Analytical and Numerical Solutions

New Conformable P-Type $(3+1)$-Dimensional Evolution Equation and its Analytical and Numerical Solutions

Dynamical behaviors of vector localized wave solutions for the coupled modified Korteweg-de Vries equations

Analyzing specific waves and various dynamics of multi-peakons in (3+1)-dimensional p-type equation using a newly created methodology

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