QuasiOneDimensional Magnetic Solitons Riemann Problem, Solitons, and Inverse Scattering Method

Despite the considerable theoretical and practical interest [1-14], there are very few monographs that cover, in sufficient depth, the nonlinear dynamics of magnetic solitons. The book offers to fill this gap to the best advantage. The monograph contains a complete presentation of the current state of the theory of quasi-one-dimensional magnetic solitons. Apart from the traditional description of nonlinear dynamics using the Landau-Lifshitz equations, the Andreev-Volkov-Marchenko-Zheltukhin models of phenomenological Lagrangians of spin waves are incorporated for the first time. The text elucidates the most effective techniques for integrating nonlinear partial differential equations (the inverse scattering method and "dressing" method), through examples that demonstrate  the construction and analysis of soliton solutions of ferromagnet models exhibiting various types of magnetic anisotropy, alongside unique solitons in multi-sublattice magnets, magnetic films, and strip domain structures. 
The discussion of specific problems includes comprehensive computations and universal methodological techniques, a complete analysis of the structure and properties of various solitons. This makes the book useful both for qualified researchers and for senior university students.

Alexander B. Borisov, Ph.D., Professor and D.habil., is the Head of the scientific direction “Theory of solitons and nonlinear phenomena in condensed matter” at the Mikheev Institute of Metal Physics of the Russian Academy of Sciences (Yekaterinburg), an Associate Member of the Russian Academy of Sciences, and an author and co-author of more than 120 scientific papers and several monographs.

Vladimir V. Kiselev, Dr. Sci. (Phys.-Math) and D.habil., is the Head Research Scientist at the sector “Theory of Nonlinear Phenomena” at the Mikheev Institute of Metal Physics of the Russian Academy of Sciences. Research interests: nonlinear phenomena in condensed matter physics, soliton theory. He is an author and co-author of more than 100 scientific papers and five monographs.

The authors have many years of experience in the theoretical description of nonlinear phenomena in magnetic, elastic, and magneto-elastic media. In the theory of solitons, A.B. Borisov developed the inverse scattering method and "dressing" method (jointly with V.V. Kiselev) for integrable nonlinear equations with an elliptic Lax pair, underlying magnetic solitons predicted and described within the Andreev-Volkov-Marchenko-Zheltukhin chiral models. The monograph broadens the concept of a soliton to encompass a diverse range of quasi-one-dimensional magnets, including under a nontrivial background as an inhomogeneous pumping wave or a stripe domain structure. The authors are currently working on what is to become the second volume of the book proposed here. That second volume will be devoted to two- and three-dimensional topological defects, solitons, and textures in magnets.