New Trends in Nonlinear Dynamics and Nonautonomous Solitons

Dear Colleagues,

Nonlinear dynamics is an ever-expanding field with a wide range of applications in applied mathematics, physics, biology, and engineering, collectively referred to as the nonlinear science. Nonlinear dynamical systems are commonly classified as autonomous if the independent variable does not appear explicitly in evolution equations and nonautonomous systems if, for example, the variable coefficients depend explicitly on time.

In recent years, significant progress has been achieved in two areas of nonlinear science: (1) further development of the nonisospectral generalization of the inverse scattering transform method with a variable spectral parameter, and the important application of this method to the study of new higher-order nonlinear evolution equations, and (2) search for hidden symmetry reduction methods in the soliton theory, especially in nonautonomous physical systems from nonlinear optics, hydrodynamics, and plasma physics to nonlinear matter waves in Bose–Einstein condensates. The so-called nonautonomous solitons arising in nonautonomous physical systems confirm the basic property of classical solitons to interact elastically, but they exhibit new properties: they propagate with varying amplitudes and velocities adapted both to external potentials and to changes in dispersion and nonlinearity.

The main purposes of this Special Issue are to provide an overview of recent ongoing progress and new trends in nonlinear dynamics and solitons, and to stimulate novel studies in the field. This Special Issue welcomes contributions from a wide range of disciplines related to nonlinear waves in nature, including, but not limited to, the inverse scattering transform and AKNS methods, computational modeling and machine learning, novel higher-order nonlinear evolution equations, soliton control and eigenvalue communications, soliton self-compression and supercontinuum generation, modulation instability, nonautonomous and spatial solitons, new and stimulating analogies with nonlinear waves in BEC, ocean, biological, and molecular systems, solitons in DNA, and other nonlinear structures in nature.

All works, such as original articles, reviews, and stimulating proposals, in all areas of nonlinear waves dynamics are welcome to be submitted to this Special Issue. Submitted papers should satisfy the general requirements of Mathematics, with particular emphasis on new analytical or numerical methods for solving challenging problems.

Prof. Dr. Tatyana L. Belyaeva
Prof. Dr. Vladimir Serkin
Prof. Dr. Lubomir Miltchev Kovachev
Guest Editors

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• mathematical physics
• nonlinear wave theory
• optics and Photonics
• nonlinear dynamics and solitary waves
• autonomous and nonautonomous dynamical systems
• nonlinear evolution equations and modulational instability
• completely integrable and nonintegrable novel mathematical models
• inverse scattering transform with varying spectral parameters
• nonautonomous solitons
• hidden symmetry reductions
• mathematics of soliton supercontinuum
• mathematical modeling and numerical methods for solving new evolution equations
• mathematical modeling using machine learning algorithms, approaches, and architectures of neural networks