Recent Developments for Nonlinear PDEs, Symmetries and Integrabilities
A special issue of Axioms (ISSN 2075-1680).
Deadline for manuscript submissions: 20 September 2026 | Viewed by 43
Special Issue Editors
Interests: integrable system; soliton equation; stability analysis; nonlinear dynamics; asymptotic analysis; nonlinear partial differential equation
Special Issue Information
Dear Colleagues,
This Special Issue highlights recent advances in nonlinear partial differential equations (PDEs), symmetries, and integrabilities, spanning core and emerging themes in the field. It encompasses foundational topics such as well-posedness, variational problems, and stability analysis, which underpin the validity and robustness of nonlinear models. Complementing theoretical frameworks, numerical methods and deep learning provide innovative tools for approximation and data-driven solutions, while research on dynamical behaviors—such as bifurcations and long-time evolution—unveils the inherent complexity of nonlinear systems. Extensions to stochastic partial differential equations (PDEs) and fractional PDEs address key challenges of nonlocality and uncertainty, whereas symmetry analysis and integrable systems—leveraging tools like Lax pairs and conservation laws—remain pivotal to deciphering solvable structures. For integrability methods specifically—including the Hirota method, Darboux transformations, inverse scattering transform, and Riemann–Hilbert techniques—elucidations of their associated coherent structures (e.g., solitons, rogue waves, and breathers) are also highly encouraged. This Issue brings together original research and reviews, fostering cross-disciplinary progress for researchers in mathematics, physics, and engineering.
Prof. Dr. Liming Ling
Prof. Dr. Xueke Pu
Guest Editors
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Keywords
- nonlinear PDEs
- symmetries
- integrability
- well-posedness
- variational problems
- stability analysis
- numerical methods
- deep learning method
- exact solution
- direct ansatz method
- Hirota method
- Darboux transformation
- inverse scattering method
- Riemann-Hilbert method
- stochastic partial differential equations
- fractional partial differential equations
- conservation laws
- Lax pair
- solitons
- rogue waves
- breathers
- Painlevé analysis
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