Solitons in a nonlinear model of spin transport in helical molecules

We study an effective integrable nonlinear model describing an electron moving along the axis of a deformable helical molecule. The helical conformation of dipoles in the molecular backbone induces an unconventional Rashba-like interaction that couples the electron spin with its linear momentum. In addition, a focusing nonlinearity arises from the electron-lattice interaction, enabling the formation of a variety of stable solitons such as bright solitons, breathers, and rogue waves. A thorough study of the soliton solutions for both focusing and defocusing nonlinear interaction is presented and discussed.

Figure 1

Squared modulus of the upper component of a two-soliton solution $|{\chi }_1^{\left[2\right]}{|}^2$ as a function of $\xi$ and $t$. Parameters are $g=2,{\theta }_0=0.5,{\theta }_1=1,{\theta }_2=1.2,s=1,j_0=1$, and $a_1=a_2=1$.

Figure 2

Squared modulus of the upper component of a rogue wave I. Parameters are $g=-2,{\theta }_0=0.5,s=1$, and $h_0=1.5$.

Figure 3

Squared modulus of the upper component of a rogue wave II. Parameters are $s=1,g=-2,{\theta }_0=0.5$, and $h_0=0.7$.