Non-chaotic dynamics for Yang-Baxter deformed $\text{AdS}_{4}\times \text{CP}^{3}$ superstrings

We explore a novel class of Yang-Baxter deformed AdS$_{4}$ $\times$ CP$^{3}$ backgrounds [Jour. High Ener. Phys. \textbf{01} (2021) 056] which exhibit a non-chaotic dynamics for (super)strings those are propagating over it. We exploit the Kovacic's algorithm to analytically study the (non-)integrability of the string sigma models over these deformed backgrounds. We also study the dynamics of the strings numerically where we probe the classical phase space of these (semi)classical strings and calculate various chaos indicators. These include studying the Poincar\'{e} sections and estimating the Lyapunov exponents. We find evidences which confirm an integrable phase space dynamics in the (semi)classical limit. Moreover, our analytical results find perfect matching with the numerical studies.