Exact solution of a multicomponent coupled spin model

Maxime Foucher, Laurent Delisle, Amine Jaouadi

Multicomponent nonlinear Schrödinger equations constitute fundamental models for coherent matter waves in multicomponent Bose--Einstein condensates, spinor quantum fluids, and vector nonlinear optical systems. We develop a vector formulation of the Hirota bilinear formalism for the completely integrable Manakov system that treats the coupled nonlinear Schrödinger equations directly at the vector level rather than through the conventional component-wise decomposition. This framework naturally retains the intrinsic multicomponent representation of the model while providing compact analytical expressions for exact vector soliton solutions. Within this approach, we systematically construct bright, dark, and mixed one-, two-, and three-soliton solutions and show how the underlying vector structure provides a unified description of their nonlinear interactions. In particular, the proposed formalism makes the coupling between the different components explicit while preserving the geometric organization of the vector system throughout the bilinearization procedure. Beyond its analytical simplicity, the framework offers a natural perspective for the study of coherent multicomponent nonlinear excitations and provides a foundation for extending vector Hirota methods to other classes of exact solutions, including rogue waves, periodic waves, and rational solutions.

A. R. Kessel, Raoul Rashidovich Nigmatullin, Airat A. Khamzin +1 more

M. C. Cambiaggio, Angelo Plastino

Vadym E. Vekslerchik, Víctor M. Pérez‐García

We find the explicit solution of the so-called two-mode model for multicomponent Bose-Einstein condensates. We prove that all the solutions are constants or periodic functions and give explicit formulae for them.

Antônio Sérgio Teixeira Pires

Akira Kawaguchi, Tatsuya Fujii, Norio Kawakami

The NMR relaxation rate $1/T_{1}$ is studied for one-dimensional multicomponent spin-orbital systems. By combining the bosonization techniques and the exact solution of the SU($n$) model, we evaluate the power-law exponent and the enhancement factor for $1/T_1$ at low temperatures. We discuss how the band splitting affects the relaxation rate, and find that $1/T_{1}$ may be enhanced around the critical value of the band splitting. The crossover behavior in $1/T_1$ around the critical point is discussed in terms of the low-frequency dynamical spin susceptibility. The effect of the hole-doping is also addressed.