Topological solitons in nondegenerate one-component chains

Area of Science:

• Condensed matter physics
• Nonlinear dynamics
• Materials science

Background:

• Topological solitons are stable, particle-like excitations in nonlinear systems.
• Their existence in one-component chains with specific potentials is theoretically explored.
• Understanding soliton behavior is crucial for applications in materials science and information transfer.

Purpose of the Study:

• To prove the existence and stability of topological solitons in one-component chains.
• To analytically and numerically investigate the properties of these solitons.
• To explore the potential role of soliton propagation in structural transformations.

Main Methods:

• Theoretical analysis of competing nonlinear potentials (V1 and V2).
• Analytical derivation of solitonic solutions for piecewise-parabolic potentials.
• Numerical simulations for smoothened nearest-neighbor potentials (V(1,delta)).
• Comparison of numerical results with analytical estimates for soliton velocity and width.

Main Results:

• Existence and stability of topological solitons are confirmed.
• Analytical solutions were found for specific potential forms.
• Numerical simulations showed good agreement with analytical predictions.
• Solitons exhibit unique velocity and maintain constant profiles under smooth potential conditions.
• Inelastic recombination of solitons with opposite signs was observed.

Conclusions:

• Topological solitons can exist and remain stable in one-component chains with competing potentials.
• Soliton propagation is characterized by unique velocity and stable profiles.
• Soliton interactions are inelastic, leading to recombination.
• Soliton dynamics may represent a fundamental mechanism for structural transformations in these chains.