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A conservative Fourier pseudospectral algorithm for the nonlinear Schrdinger equation

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【作者】 吕忠全； 张鲁明； 王雨顺；

【Author】 Lv Zhong-Quan;Zhang Lu-Ming;Wang Yu-Shun;College of Science, Nanjing University of Aeronautics and Astronautics;College of Science, Nanjing Forestry University;School of Mathematical Sciences, Nanjing Normal University;

【机构】 College of Science, Nanjing University of Aeronautics and Astronautics； College of Science, Nanjing Forestry University； School of Mathematical Sciences, Nanjing Normal University；

【摘要】 In this paper, we derive a new method for a nonlinear Schr ¨odinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in · 2norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.

【Abstract】 In this paper, we derive a new method for a nonlinear Schr ¨odinger system by using the square of the first-order Fourier spectral differentiation matrix D1 instead of the traditional second-order Fourier spectral differentiation matrix D2 to approximate the second derivative. We prove that the proposed method preserves the charge and energy conservation laws exactly. A deduction argument is used to prove that the numerical solution is second-order convergent to the exact solutions in · 2norm. Some numerical results are reported to illustrate the efficiency of the new scheme in preserving the charge and energy conservation laws.

【关键词】 Fourier pseudospectral method； Schrdinger equation； conservation law； convergence；
【Key words】 Fourier pseudospectral method； Schrdinger equation； conservation law； convergence；
【基金】 Project supported by the National Natural Science Foundation of China(Grant Nos.11271195,41231173,and 11201169);the Postdoctoral Foundation of Jiangsu Province of China(Grant No.1301030B);the Open Fund Project of Jiangsu Key Laboratory for NSLSCS(Grant No.201301);the Fund Project for Highly Educated Talents of Nanjing Forestry University(Grant No.GXL201320)
  • 【文献出处】 Chinese Physics B ,中国物理B , 编辑部邮箱 ,2014年12期
  • 【分类号】O175
  • 【被引频次】7
  • 【下载频次】55
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