Soliton Theory and Integrable Systems in Mathematical Physics

Dear Colleagues,

Integrable systems and nonlinear evolution equations arise in several areas of modern physics. Distinguishing features of integrable models are their many infinitely conserved quantities and soliton solutions. However, several quasi-integrable models with solitary waves, which resemble the true solitons, present relevant physical applications. So, important methods and techniques for dealing with general nonlinear systems have been introduced. Recently, through analytical and numerical methods, the quasi-integrability approach has been introduced to deal with some deformations of integrable systems.

The theory of integrable systems encompasses algebraic, geometric, and analytic approaches. In addition, numerical simulation techniques have become useful tools to understand the soliton phenomena since the stability and collision of solitary waves deserve careful examinations. This theory exhibits many connections to mathematics, physics, and other nonlinear sciences, and much of the interest resides in their various applications. In this Special Topic, we seek to focus on the various distinct formal definitions of integrability, such as a Lax integrable model, a Painlevé integrable model, an inverse scattering transform (IST) integrable model, a consistent Riccati expansion (CRE) integrable model, and a symmetry integrable system defined as possessing many infinite symmetries. Moreover, the quasi-integrable modifications deserve to be examined in the context of the recursion operators, generalized local and non-local symmetries, anomalous zero-curvature, and Riccati-type pseudopotential approaches. We also invite papers that employ numerical techniques in order to simulate the soliton phenomena, such as pseudo-spectral, time-splitting, relaxation, and other methods.

This Special Issue will focus on the following items, as well as many other relevant topics:

• Integrable and quasi-integrable systems;
• Symmetries of integrable systems;
• Integrable nonlocal nonlinear equations;
• Stability of solitary waves;
• Riccati-type pseudo-potentials and quasi-integrability;
• Anomalous Lax pair and zero curvature representations;
• Numerical and analytical methods;
• Complex and non-Hermitian extensions of soliton theory;
• Nonlinear waves in PT-symmetric systems.

Prof. Dr. Harold Blas
Guest Editor

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• numerical simulation
• solitons
• quasi-integrability
• nonlinear evolutions
• symmetries
• conserved charges