arXiv subjects
Publications and source records attributed to M. Wadati.
In this paper, we have studied the integrability nature of a system of three coupled Gross-Pitaevskii type nonlinear evolution equations arising in the context of spinor Bose-Einstein condensates by applying the Painlevé singularity structure analysis. We show that only for two sets of parametric choices, corresponding to the known integrable cases, the system passes the Painlevé test.
The Lax pair for a derivative nonlinear Schrödinger equation proposed by Chen-Lee-Liu is generalized into matrix form. This gives new types of integrable coupled derivative nonlinear Schrödinger equations. By virtue of a gauge transformation, a new multi-component extension of a derivative nonlinear Schrödinger equation proposed by Kaup-Newell is also obtained.
By using the fact that Polychronakos-like models can be obtained through the `freezing limit' of related spin Calogero models, we calculate the exact spectrum as well as partition function of SU(m|n) supersymmetric Polychronakos (SP) model. It turns out that, similar to the non-supersymmetric case, the spectrum of SU(m|n) SP model is also equally spaced. However, the degeneracy factors of corresponding energy levels crucially depend on the values of bosonic degrees of freedom (m) and fermionic degrees of freedom (n). As a result, the partition functions of SP models are expressed through some novel q-polynomials. Finally, by interchanging the bosonic and fermionic degrees of freedom, we obtain a duality relation among the partition functions of SP models.
A system of semi-discrete coupled nonlinear Schrödinger equations is studied. To show the complete integrability of the model with multiple components, we extend the discrete version of the inverse scattering method for the single-component discrete nonlinear Schrödinger equation proposed by Ablowitz and Ladik. By means of the extension, the initial-value problem of the model is solved. Further, the integrals of motion and the soliton solutions are constructed within the framework of the extension of the inverse scattering method.
Generalization of the modified KdV equation to a multi-component system, that is expressed by $(\partial u_i)/(\partial t) + 6 (\sum_{j,k=0}^{M-1} C_{jk} u_j u_k) (\partial u_i)/(\partial x) + (\partial^3 u_{i})/(\partial x^3) = 0, i=0, 1, ..., M-1 $, is studied. We apply a new extended version of the inverse scattering method to this system. It is shown that this system has an infinite number of conservation laws and multi-soliton solutions. Further, the initial value problem of the model is solved.