非局域非线性薛定谔方程的对称性保持和对称性破缺亮、暗和反暗孤子解
On symmetry preserving and symmetry broken bright, dark and antidark soliton solutions of nonlocal nonlinear Schrödinger equation
摘要：
构造了一类非局域非线性薛定谔方程的保对称和对称破缺的N-亮、暗和反暗孤子解.为了得到这些解，我们在达布变换（DT）方法中使用适当的本征函数。我们给出了一个和两个明孤子解，并证明了只有当我们将光场和宇称变换复共轭场结合起来时，它们才具有稳定的结构。进一步，我们利用DT方法导出了两个暗/反暗孤子解。与亮孤子的情况不同，暗/反暗孤子解分别对光场和宇称变换共轭光场表现出稳定的结构。在暗/反暗孤子解的情况下，我们观察到一个对比的行为之间的包络线的字段和宇称变换复共轭包络线的字段。对于一个特定的参数选择，我们得到暗（反暗）孤子的领域，而宇称变换复共轭场表现出反暗（暗）孤子。由于这个令人惊讶的结果，场和PT变换的复共轭场都表现出16种不同的碰撞场景组合。通过对暗孤子和反暗孤子的渐近分析，对场和宇称变换复共轭场中暗孤子和反暗孤子的参量区域进行了分类。进一步给出了$2N$ -暗/反暗孤子解公式，并证明了该解可能存在$2^{2N}\times 2^{2N}$碰撞组合.
英文摘要：
We construct symmetry preserving and symmetry broken N-bright, dark and antidark soliton solutions of a nonlocal nonlinear Schrödinger equation. To obtain these solutions, we use appropriate eigenfunctions in Darboux transformation (DT) method. We present explicit one and two bright soliton solutions and show that they exhibit stable structures only when we combine the field and parity transformed complex conjugate field. Further, we derive two dark/antidark soliton solution with the help of DT method. Unlike the bright soliton case, dark/antidark soliton solution exhibits stable structure for the field and the parity transformed conjugate field separately. In the dark/antidark soliton solution case we observe a contrasting behaviour between the envelope of the field and parity transformed complex conjugate envelope of the field. For a particular parametric choice, we get dark (antidark) soliton for the field while the parity transformed complex conjugate field exhibits antidark (dark) soliton. Due to this surprising result, both the field and PT transformed complex conjugate field exhibit sixteen different combinations of collision scenario. We classify the parametric regions of dark and antidark solitons in both the field and parity transformed complex conjugate field by carrying out relevant asymptotic analysis. Further we present $2N$-dark/antidark soliton solution formula and demonstrate that this solution may have $2^{2N}\times 2^{2N}$ combinations of collisions.
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