Degenerate Four Virtual Soliton Resonance for KP-II

By using disipative version of the second and the third members of AKNS hierarchy, a new method to solve 2+1 dimensional Kadomtsev-Petviashvili (KP-II) equation is proposed. We show that dissipative solitons (dissipatons) of those members give rise to the real solitons of KP-II. From the Hirota bilinear form of the SL(2,R) AKNS flows, we formulate a new bilinear representation for KP-II, by which, one and two soliton solutions are constructed and the resonance character of their mutual interactions is studied. By our bilinear form, we first time created four virtual soliton resonance solution for KP-II and established relations of it with degenerate four-soliton solution in the Hirota-Satsuma bilinear form for KP-II.Comment: 10 pages, 5 figures, Talk on International Conference Nonlinear Physics. Theory and Experiment. III, 24 June-3 July, 2004, Gallipoli(Lecce), Ital

Young diagrams and N-soliton solutions of the KP equation

We consider $N$-soliton solutions of the KP equation, (-4u_t+u_{xxx}+6uu_x)_x+3u_{yy}=0 . An $N$-soliton solution is a solution $u(x,y,t)$ which has the same set of $N$ line soliton solutions in both asymptotics $y\to\infty$ and $y\to -\infty$. The $N$-soliton solutions include all possible resonant interactions among those line solitons. We then classify those $N$-soliton solutions by defining a pair of $N$-numbers $({\bf n}^+,{\bf n}^-)$ with ${\bf n}^{\pm}=(n_1^{\pm},...,n_N^{\pm}), n_j^{\pm}\in\{1,...,2N\}$, which labels $N$ line solitons in the solution. The classification is related to the Schubert decomposition of the Grassmann manifolds Gr$(N,2N)$, where the solution of the KP equation is defined as a torus orbit. Then the interaction pattern of $N$-soliton solution can be described by the pair of Young diagrams associated with $({\bf n}^+,{\bf n}^-)$. We also show that $N$-soliton solutions of the KdV equation obtained by the constraint $\partial u/\partial y=0$ cannot have resonant interaction.Comment: 22 pages, 5 figures, some minor corrections and added one section on the KdV N-soliton solution

Dyonic Non-Abelian Vortices

We study three-dimensional Yang-Mills-Higgs theories with and without a Chern-Simons interaction. We find that these theories admit a rich spectrum of vortex solitons carrying both a topological charge and a global flavour charge. We further derive a low-energy description of the vortex dynamics from a gauged linear sigma model on the vortex worldline.Comment: 16 pages, 3 figures; references added in section

Chern - Simons Gauge Field Theory of Two - Dimensional Ferromagnets

A Chern-Simons gauged Nonlinear Schr\"odinger Equation is derived from the continuous Heisenberg model in 2+1 dimensions. The corresponding planar magnets can be analyzed whithin the anyon theory. Thus, we show that static magnetic vortices correspond to the self-dual Chern - Simons solitons and are described by the Liouville equation. The related magnetic topological charge is associated with the electric charge of anyons. Furthermore, vortex - antivortex configurations are described by the sinh-Gordon equation and its conformally invariant extension. Physical consequences of these results are discussed.Comment: 15 pages, Plain TeX, Lecce, June 199

Tunable Spin-Flop Transition in Artificial Ferrimagnets

Spin-flop transition (SFT) consists in a jump-like reversal of antiferromagnetic (AF) lattice into a noncollinear state when the magnetic field increases above the critical value. Potentially the SFT can be utilized in many applications of a rapidly developing AF spintronics. However, the difficulty of using them in conventional antiferromagnets lies in (a) too large switching magnetic fields (b) the need for presence of a magnetic anisotropy, and (c) requirement to apply magnetic field along the correspondent anisotropy axis. In this work we propose to use artificial ferrimagnets (FEMs) in which the SFT occurs without anisotropy and the transition field can be lowered by adjusting exchange coupling in the structure. This is proved by experiment on artificial Fe-Gd FEMs where usage of Pd spacers allowed us to suppress the transition field by two orders of magnitude. © 2021 authors. Published by the American Physical Society. Open access publication funded by the Max Planck Society.We thank A. B. Drovosekov, D. I. Kholin, and D. Cortie for fruitful discussion of the results. This work is partially based on experiments performed at the NREX instrument operated by the Max Planck Society at the MLZ, Garching, Germany and supported by the Deutsche Forschungsgemeinschaft (Project No. 107745057-TRR80). Research in Ekaterinburg was performed within the state assignment of Minobrnauki of Russia (theme “Spin” No. AAAA-A18-118020290104-2) and was partly supported by Russian Foundation for Basic Research (Project No. 19-02-00674)