Saved in:
| Main Authors: | , |
|---|---|
| Format: | Preprint |
| Published: |
2025
|
| Subjects: | |
| Online Access: | https://arxiv.org/abs/2512.04526 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1866918318486585344 |
|---|---|
| author | Zhong, D. Y. Wang, G. Q. |
| author_facet | Zhong, D. Y. Wang, G. Q. |
| contents | We develop a contact-geometric framework for dissipative nonlinear field theories by extending the least constraint theorem to complex fields and establishing a rigorous link with probability measures. The Complex Ginzburg-Landau Equation serves as a paradigmatic example, yielding a dissipative Contact Hamilton-Jacobi equation that governs the evolution of the action functional. Through canonical transformation and travelling-wave reduction, exact Jacobi elliptic solutions are obtained, revealing a continuous transition from periodic periodons to localised solitons. Probabilistic analysis identifies a universal switching line separating dynamical regimes and uncovers a first-order periodon-soliton phase transition with a hysteresis loop. The conserved contact potential emerges as the key geometric quantity governing pattern formation in dissipative media, analogous to energy in conservative systems. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2512_04526 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | Dynamics of Dissipative Nonlinear Systems: A Study via 2D CGLE by Contact Geometry Zhong, D. Y. Wang, G. Q. Pattern Formation and Solitons We develop a contact-geometric framework for dissipative nonlinear field theories by extending the least constraint theorem to complex fields and establishing a rigorous link with probability measures. The Complex Ginzburg-Landau Equation serves as a paradigmatic example, yielding a dissipative Contact Hamilton-Jacobi equation that governs the evolution of the action functional. Through canonical transformation and travelling-wave reduction, exact Jacobi elliptic solutions are obtained, revealing a continuous transition from periodic periodons to localised solitons. Probabilistic analysis identifies a universal switching line separating dynamical regimes and uncovers a first-order periodon-soliton phase transition with a hysteresis loop. The conserved contact potential emerges as the key geometric quantity governing pattern formation in dissipative media, analogous to energy in conservative systems. |
| title | Dynamics of Dissipative Nonlinear Systems: A Study via 2D CGLE by Contact Geometry |
| topic | Pattern Formation and Solitons |
| url | https://arxiv.org/abs/2512.04526 |