Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order

We investigate the nonlinear spin dynamics of an anisotropic Heisenberg ferromagnetic spin chain with octupole-dipole interaction in the semiclassical limit using the coherent-state method combined with the Holstein-Primakoff bosonic representation of spin operators. The dynamics is found to be governed by a generalized nonlinear Schr\"odinger equation in the continuum limit. For specific values of the exchange, octupole-dipole interactions, and also of the anisotropy parameters, through Painlev\'e singularity structure analysis, we have identified an integrable spin chain model with soliton spin excitations. We carry out a multiple scale perturbation analysis to find the discreteness effect on the soliton excitations in the more general nonintegrable case.

Soliton spin excitations in an anisotropic Heisenberg ferromagnet with octupole-dipole interaction

Faraday waves in a cigar-shaped Bose-Einstein condensate are created. It is shown that periodically modulating the transverse confinement, and thus the nonlinear interactions in the BEC, excites small amplitude longitudinal oscillations through a parametric resonance. It is also demonstrated that even without the presence of a continuous drive, an initial transverse breathing mode excitation of the condensate leads to spontaneous pattern formation in the longitudinal direction. Finally, the effects of strongly driving the transverse breathing mode with large amplitude are investigated. In this case, impact-oscillator behavior and intriguing nonlinear dynamics, including the gradual emergence of multiple longitudinal modes, are observed.

http://absimage.aps.org/image/DAMOP07/MWS_DAMOP07-2007-000311.pdf

Observation of Faraday Waves in a Bose-Einstein Condensate

In this paper, we will investigate a famous model of nonlinear sciences namely (2 + 1)-dimensional nonlinear spin dynamics of Heisenberg ferromagnetic spin chains (HFSC) model for the evaluation of...

Conserved quantities along with Painlevé analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model

A general two-coupled nonlinear Schrodinger system is investigated with symbolic computation. The system is regarded to be a more general model than other coupled nonlinear Schrodinger systems since its coefficients of the self-phase modulation, cross-phase modulation, and four-wave mixing terms are arbitrary. Painleve-integrability associated with the system is examined by means of Painleve test. As a result, Painleve–Backlund transformation is constructed with truncating the Laurent series at the constant level term. In addition, a family of explicit solutions corresponding to the vacuum solutions are derived through the Painleve–Backlund transformation.

Painlevé-integrability and explicit solutions of the general two-coupled nonlinear Schrödinger system in the optical fiber communications

We investigate the nonlinear spin dynamics of (2+1)-dimensional Heisenberg ferromagnetic (FM) spin chains with bilinear and anisotropic interactions in the semiclassical limit using the coherent state ansatz combined with the Holstein–Primakoff (HP) bosonic representation of spin operators. In the continuum limit the dynamics is found to be governed by a new integrable nonlinear Schrodinger type equation in (2+1) dimensions. The integrability of the equation is studied by constructing Lax pair of operators. The multisoliton solution is generated through the Darboux transformation. We also propose a model representing the (2+1)-dimensional inhomogeneous Heisenberg FM spin chain and the effect of inhomogeneity is understood by performing a perturbation analysis. Finally, the modulation instability aspects are discussed via analytic solutions and graphical illustrations.

https://iopscience.iop.org/article/10.1088/0031-8949/89/6/065204/pdf

An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

We propose a generalized Davydov model with higher order molecular interactions and excitations of dipole and quadrupole types with appropriate nonlinear coupling with phonons and study the underlying nonlinear molecular coherent excitations under continuum approximation in terms of solitons to represent energy transfer along the hydrogen bonding spines of the alpha helical proteins. We have identified six specific models at different orders of continuum approximation for particular choice of parameters under this new generalized model that support energy transfer in the form of solitons. In the general case, we have constructed the perturbed soliton and the perturbation analysis shows that the velocity and amplitude of the soliton do not change.

A generalized Davydov soliton model for energy transfer in alpha helical proteins

We consider discrete and continuum models of alpha helical proteins with different orders of molecular excitations and interactions. In both the cases integrable models were identified for specific choice of parameters and the elementary excitations expressed in terms of solitons. Also, equivalent integrable Heisenberg spin systems were obtained.

M.M. Latha

Papers

An integrable model of (2+1)-dimensional Heisenberg ferromagnetic spin chain and soliton excitations

A generalized Davydov soliton model for energy transfer in alpha helical proteins

Soliton in discrete and continuum alpha helical proteins with higher-order excitations

Soliton in alpha helical proteins with interspine coupling at higher order

Soliton in discrete and continuum alpha helical proteins with interspine coupling