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Multiple lump and interaction solutions for fifth-order variable coefficient nonlinear-Schrödinger dynamical equation
S T R Rizvi1, Aly R Seadawy2, K Ali1
1Department of Mathematics, COMSATS University Islamabad, Lahore Campus, Lahore, Pakistan.
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.
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.
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