In this paper, the nonlinear wave solutions for Gross–Pitaevskii equation on the periodic wave background are investigated by Darboux-Bäcklund transformation, from which the soliton and breather wave solutions on the Jacobi elliptic cn and dn functions backgrounds are derived. The corresponding evolutions and dynamical properties of nonlinear wave solutions under different parameters are discussed. These results reported in this paper may raise the possibility of related experiments and potential applications in nonlinear science fields, such as nonlinear optics, oceanography and so on.

中文翻译：

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Gross-Pitaevskii 方程雅可比椭圆函数周期背景上的局部激励


本文通过Darboux-Bäcklund变换研究了周期波背景上Gross-Pitaevskii方程的非线性波解，并推导了雅可比椭圆cn和dn函数背景上的孤子波和呼吸波解。讨论了不同参数下非线性波解的相应演化和动力学性质。本文报道的这些结果可能会提高相关实验的可能性以及在非线性光学、海洋学等非线性科学领域的潜在应用。