Nonlocal integrable systems have attracted increasing interest from the international nonlinear science research community in the past few years, which feature distinctive types of nonlinear dynamical behaviors and properties. Physical backgrounds related to nonlocal systems are also explored from various physical fields, such as magnetic structure, nonmagnetic artificial materials, loop quantum cosmology, and multi-place physics. Those new discoveries trigger renewed interest in the study of nonlocal integrable systems. Subsequently, various types of nonlocal integrable systems and their corresponding dynamical properties and exact solutions become hot topics and will be extensively investigated. At the same time, some classical methods developed in local integrable systems, such as the Hirota bilinear method, Darboux transformation, and linear superposition ansatze, are applied to nonlocal integrable systems with some modifications.
However, the primary problems on nonlocal integrable systems, including the well-posedness theory of Cauchy problems, remain open and need to be answered. The physical backgrounds of those studied nonlocal systems are rather weak. The excitation mechanism and mutual conversion relationship of various types of nonlinear waves, including soliton, breather, and rogue waves, is not yet crystal clear. Some classical and well-established methods, such as the Riemann-Hilbert and inverse scattering techniques, are very difficult to generalize to deal with nonlocal integrable systems. The construction of N-soliton solutions and nonlinear superposition formulas, especially for high-order nonlocal equations, is a very challenging task. Therefore, mathematical structures underlying nonlocal integrable systems and their corresponding nonlinear wave solutions are very interesting and need to be further investigated.
To develop related mathematical theories that hope to reflect diverse aspects of nonlocal integrable systems and further research of their corresponding physical applications, we seek high-quality original research papers on topics including but not limited to:
• Nonlocal integrable and partially integrable models in physics;
• Nonlinear wave phenomena described by nonlocal integrable systems;
• Nonlinear dynamical features of nonlocal integrable systems;
• Symbolic computation and numerical simulation of nonlocal integrable systems;
• Applications of Riemann-Hilbert problems and machine learning to nonlocality;
• Discrete nonlocal integrable systems.
Nonlocal integrable systems have attracted increasing interest from the international nonlinear science research community in the past few years, which feature distinctive types of nonlinear dynamical behaviors and properties. Physical backgrounds related to nonlocal systems are also explored from various physical fields, such as magnetic structure, nonmagnetic artificial materials, loop quantum cosmology, and multi-place physics. Those new discoveries trigger renewed interest in the study of nonlocal integrable systems. Subsequently, various types of nonlocal integrable systems and their corresponding dynamical properties and exact solutions become hot topics and will be extensively investigated. At the same time, some classical methods developed in local integrable systems, such as the Hirota bilinear method, Darboux transformation, and linear superposition ansatze, are applied to nonlocal integrable systems with some modifications.
However, the primary problems on nonlocal integrable systems, including the well-posedness theory of Cauchy problems, remain open and need to be answered. The physical backgrounds of those studied nonlocal systems are rather weak. The excitation mechanism and mutual conversion relationship of various types of nonlinear waves, including soliton, breather, and rogue waves, is not yet crystal clear. Some classical and well-established methods, such as the Riemann-Hilbert and inverse scattering techniques, are very difficult to generalize to deal with nonlocal integrable systems. The construction of N-soliton solutions and nonlinear superposition formulas, especially for high-order nonlocal equations, is a very challenging task. Therefore, mathematical structures underlying nonlocal integrable systems and their corresponding nonlinear wave solutions are very interesting and need to be further investigated.
To develop related mathematical theories that hope to reflect diverse aspects of nonlocal integrable systems and further research of their corresponding physical applications, we seek high-quality original research papers on topics including but not limited to:
• Nonlocal integrable and partially integrable models in physics;
• Nonlinear wave phenomena described by nonlocal integrable systems;
• Nonlinear dynamical features of nonlocal integrable systems;
• Symbolic computation and numerical simulation of nonlocal integrable systems;
• Applications of Riemann-Hilbert problems and machine learning to nonlocality;
• Discrete nonlocal integrable systems.
