以下为句子列表：
英文: Abstract: Considering the second nearest-neighbor interaction and cubic,quartic anharmonic interactions simultaneously, we employ the multiple scales method combined with a quasidiscreteness approximation to calculate the lattice vibration.It is shown tha
中文: 文摘:同时考虑次近邻谐振相互作用和三次方、四次方非谐相互作用，利用多重尺度结合准离散近似方法去计算晶格振动行为，发现一维非线性点阵中存在包络孤子及正扭结型包络孤子、反扭结型包络孤子，解释了自局域结构的幅度只取决于点阵中的固有参数的实验现象.
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英文: Treating the anharmonic terms of potential energy as perturbations, and employing the formulas for atomic displacements and Hamiltonian in phonon occupation number representation, the formulas for thermal expansion coefficients of crystal nano-wires are d
中文: 摘要将原子间相互作用势的非谐项作为微扰，运用声子数表象中的晶格原子振动位移和晶格振动哈密顿公式，推导了纳米晶体线的热膨胀系数公式，并进行了数值计算。
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英文: Energy Spectra of Spherical Anharmonic Oscillator Using Feldman Method
中文: 球四次非谐振子能谱的Feldman解
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