Invariant solutions, lie symmetry analysis, bifurcations and nonlinear dynamics of the Kraenkel-Manna-Merle system with and without damping effect
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View abstract on PubMed
Summary
This summary is machine-generated.This study explores solitary wave solutions in the Kraenkel-Manna-Merle (KMM) system for ferromagnetic materials. Researchers discovered new bright, dark, and exponential solitons, plus chaotic dynamics, advancing magnetic material science.
Area Of Science
- Nonlinear dynamics
- Condensed matter physics
- Mathematical modeling
Background
- The Kraenkel-Manna-Merle (KMM) system describes nonlinear short wave propagation in ferromagnetic materials.
- Understanding solitary wave behavior is crucial for applications in spintronics and magnetic data storage.
Purpose Of The Study
- To derive and analyze novel solitary wave solutions for the KMM system.
- To investigate the system's dynamics, including chaotic behavior and bifurcation.
- To explore potential applications in advanced material science.
Main Methods
- Lie group transformations to convert partial differential equations to ordinary differential equations (ODEs).
- Similarity invariant approach for analytical solutions of ODEs.
- Wave and Galilean transformations for system reduction and bifurcation analysis.
- Planar dynamical theory for identifying diverse soliton solutions.
Main Results
- Discovery of various solitary wave solutions: bright, dark, exponential, kink, and periodic solitons.
- Identification of multi-scroll chaotic dynamics in the presence of damping.
- Observation of off-boosting dynamics in the absence of damping.
- Visualization of soliton solutions using 2D and 3D graphs.
Conclusions
- The study successfully derived new solitary wave solutions for the KMM system.
- The findings offer insights into the complex dynamics of ferromagnetic materials.
- Results have potential implications for magnetic data storage, magnonic devices, and spintronics.
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