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Schr?dinger方程的周期孤立波解

Periodic wave solutions for Schr?dinger equation
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摘要 利用包络变换,先把复方程Schrodinger方程化为两个实方程,再运用Hirota双线性法来求解.使用通常的Hirota双线性法中的测试函数,能得到方程的N孤波解,现在把测试函数改用带周期性的三波函数来替代,得到一个超越代数方程组,然后利用数学软件Matlab求解该方程组,得到若干组解,从而求得Schrodinger方程带周期的新的周期孤波解和周期双孤立波解,进而讨论了Schrodinger方程所描述的动力系统的时空分岔问题. Using the envelope transformation,the complex Schrodinger equation was converted into two real equations,and the Hirota bilinear method was used to solve the problem.Using the test function in the usual Hirota bilinear method,the N solitary wave solution of the equation can be obtained.Now replace the test function with a cyclic three-wave function.A system of transcendental algebraic equations was obtained,and then Matlab was used to solve the system of equations,and a number of group solutions were obtained.Therefore,a new periodic solitary wave solution and a periodic double solitary wave solution of the Schrodinger equation with a period were obtained.The space-time bifurcation problem of dynamic system described by Schrodinger equation.
作者 傅海明 戴正德 FU Hai-ming;DAI Zheng-de(Department of Basic Courses,Guangzhou Hua Xia Vocational College,Guangzhou 510935,China;Department of Mathematics,Yunnan University,Kunming 650091,China)
出处 《哈尔滨商业大学学报(自然科学版)》 CAS 2019年第3期380-384,共5页 Journal of Harbin University of Commerce:Natural Sciences Edition
基金 国家自然科学基金资助项目(11361048) 广东省教育厅特色创新类项目(2017GKTSCX111)
关键词 SCHRODINGER方程 HIROTA方法 双周期波解 孤立波解 双线性型 精确解 Schrodinger equation Hirota method double periodic wave solution soliton wave solution bilinear type exact solution
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