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Multiple lump and interaction solutions for fifth-order variable coefficient nonlinear-Schrödinger dynamical

S T R Rizvi1, Aly R Seadawy2, K Ali1

  • 1Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.

Optical and Quantum Electronics
|May 2, 2022
PubMed
Summary
This summary is machine-generated.

This study investigates lump wave interactions in a fifth-order nonlinear-Schrödinger equation, revealing new analytical solutions for complex wave phenomena. The findings offer insights into nonlinear wave dynamics and their graphical representations.

Keywords:
Ansatz transformationsMultiple lump-solitonsPeriodic cross lump wavesVariable coefficient NLSE

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Area of Science:

  • Nonlinear Physics
  • Mathematical Physics
  • Wave Phenomena

Background:

  • The nonlinear-Schrödinger equation (NLSE) is a fundamental model in various fields, including optics and fluid dynamics.
  • Understanding complex wave solutions like lumps, kinks, and rogue waves is crucial for predicting nonlinear system behavior.
  • Variable coefficients in the NLSE introduce additional complexity, requiring advanced analytical techniques.

Purpose of the Study:

  • To analyze lump wave interactions with kink, periodic, and rogue waves in a fifth-order variable coefficient NLSE.
  • To derive novel analytical solutions for different types of lump solitons.
  • To explore the interaction phenomena and visualize the resulting wave patterns.

Main Methods:

  • Utilized a combination of bilinear, exponential, and trigonometric functions.
  • Employed analytical techniques to construct new solutions for the variable coefficient NLSE.
  • Applied graphical representations to illustrate the derived wave solutions and their interactions.

Main Results:

  • Successfully derived various lump soliton solutions for the studied fifth-order variable coefficient NLSE.
  • Identified and analyzed the interaction dynamics between lump waves and other wave types (kink, periodic, rogue).
  • Generated novel analytical solutions showcasing complex interaction phenomena.

Conclusions:

  • The study provides new analytical insights into lump wave behaviors and their interactions within a complex NLSE.
  • The developed methods and solutions can be applied to understand similar nonlinear wave phenomena in diverse physical systems.
  • Graphical representations aid in the visualization and comprehension of intricate nonlinear wave dynamics.