Nonlocal Cubic-Quintic Nonlinear Schrödinger Equation: Symmetry Breaking Solitons and Its Trajectory Rotation
Tóm tắt
Using two analytical methods, we derive exact and more general solutions of the nonlocal nonlinear Schrödinger equation with nonlocal cubic and nonlocal quintic terms. In the first method, equations are analyzed, and some of their mathematical and physical properties are inferred, which are then used to derive the exact stationary solutions. In the second method, we demonstrate the Darboux transformation method and construct exact and more general soliton solutions for the nonlocal NLS equation with nonlocal cubic and quintic terms. We reconsider the collisional dynamics of the nonlocal NLS equation and observe that apart from intensity redistribution in the interaction of bright and dark solitons, one also witnesses a rotation of the trajectories of the solitons. The angle of rotation can be varied by suitably manipulating the self-phase-modulation (SPM) or cross-phase-modulation (XPM) parameters and also spectral parameters. The angle of rotation of the solitons arises due to the excess energy that is injected into the dynamical system through SPM and XPM. We also notice the parallel traveling solitons due to the rotation in the soliton trajectories. These observations which exclude the quantum superposition for the field vectors may have wider ramifications in nonlinear optics, Bose–Einstein condensates, and left- and right-handed metamaterials.
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