Symmetry and Integrable Systems: Theory, Methods, and Applications

Dear Colleagues,

Symmetry and integrable systems are two fundamental concepts in mathematics and physics that have profound implications across various disciplines. Symmetry is a fundamental concept in mathematics and physics, which refers to the property of remaining invariant under certain transformations. An integrable system is a mathematical or physical system that possesses a sufficient number of conservation laws or other properties that allow its solutions to be obtained in a systematic and explicit way. Integrable systems often arise in the context of differential equations, such as KdV and NLS equations. The relationship between symmetry and integrable systems is significant. The infinite conservation laws in integrable systems always mean infinite symmetries by the famous Noether theorem. And symmetric properties can help in finding solutions and understanding the various behaviors of integrable systems. Thus, symmetry often provides insights into the structure of integrable systems, and vice versa. By studying symmetry, we can better understand the properties of integrable systems, and the study of integrable systems helps us explore the deeper implications of symmetry.

Prof. Dr. Jipeng Cheng
Guest Editor

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