Yingxin Duan

Conflicts of Interest The authors declare no conflicts of interest. Data Availability Statement No data were generated or analyzed during the current study. References 1, , and , “Bright and Dark Solitary Waves in the Presence of Third-Harmonic Generation,” Journal of the Optical Society of America B: Optical Physics 15 (1998): 1488–1496. 2, Nonlinear Optics (Academic Press, Elsevier Inc., 2008). 3 and , “Solitons due to Second Harmonic Generation,” Physics Letters A 197, no. 5–6 (1995): 407–412.

In this paper, we investigate the nonlinear Schödinger equations with cubic interactions, arising in nonlinear optics. To begin, we prove the existence results for normalized ground state solutions in the subcritical case and L 2 $$ {L}^2 $$ -supercritical case, respectively. Our proofs relies on the Concentration-compactness principle, Pohozaev manifold, and rearrangement technique.