Invariant soliton solutions for the coupled nonlinear Schrödinger type equation

Malik, Sandeep; Kumar, Sachin; Nisar, Kottakkaran Sooppy

doi:10.1016/j.aej.2022.11.003

Cited by 22 publications

(1 citation statement)

References 29 publications

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“…Therefore, NEEs are a special case of NPDEs. Evolution equations of Klein-Gordon or Schrödinger type are widely used in quantum mechanics [3,4]. Similarly, equations of advectiondiffusion type in civil engineering [5], equations such as modified Benjamin-Bona-Mahony are widely used in fluid dynamics [6], and equations such as Kadomtsev-Petviashvili equation are widely used in shallow water waves [7].…”

Section: Introductionmentioning

confidence: 99%

A study on solitary wave solutions for the Zoomeron equation supported by two-dimensional dynamics

Duran,

Yokus,

Kilinc

2023

Phys. Scr.

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This study emphasizes the importance of understanding natural phenomena through various observations and relating them to scientific studies. Nonlinear partial differential equations serve as fundamental tools for modeling these phenomena, with a focus on nonlinear evolution equations when involving time. This paper investigates the dynamics of the Zoomeron equation, highlighting not only a result derived from the KdV and Schrödinger equations but also its contribution to the modeling of Boomeron and Trappon solitons. Different analytical techniques yield various solutions for the Zoomeron equation, each offering unique insights. The behavior of the solutions generated in kink and singular soliton forms in various dynamics using the G ′ / G 2 -expansion method is investigated and compared under restrictive conditions, and the distribution of energy density is explained with the assistance of the gradient function. It is aimed at gaining a physically unique perspective by revealing the connections between the velocities of solitons produced for this equation and the effects of gradient flow directions. In addition, stability analysis for some of the solutions generated in the kink form is investigated. The structure of the paper includes method introduction, application, stability property, results and discussion, resulting in a unique perspective on understanding the physical dynamics of the Zoomeron model.

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