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| 1 | 第一类导数非线性薛定谔方程的数值模拟显示文摘利用Taylor级数展开,给出了求解第一类导数非线性薛定谔方程的CrankNicolson格式。使用该格式对该方程进行数值模拟,数值算例验证了该格式具有保持时空2阶精度的性质。最后在初值上添加微小随机扰动,观察孤子解随时间的变化情况,结果显示孤子解在初值添加微小随机扰动后变化不大,说明孤子解具有很好的稳定性。 | 李书存 曹俊杰 李文博 | 2016 | 北京信息科技大学学报(自然科学版)2016，31，3： | 6 |
| 2 | A Multi-Soliton Solution of the DNLS Equation Based on Pure Marchenko Formalism显示文摘By means of some algebraic techniques,especially the Binet-Cauchy formula,an explicit multi-soliton solution of the derivative nonlinear Schrdinger equation with vanishing boundary condition is attained based on a pure Marchenko formalism without needing the usual scattering data except for given N simple poles. The one-and two-soliton solutions are given as two special examples in illustration of the general formula of multi-soliton solution. Their effectiveness and equivalence to other approaches are also demonstrated. Meanwhile,the asymptotic behavior of the multi-soliton solution is discussed in detail. It is shown that the N-soliton solution can be viewed as a summation of N one-soliton solutions with a definite displacement and phase shift of each soliton in the whole process(from t →∞ to t → +∞ ) of the elastic collisions. | ZHOU Guoquan School of Physics and Technology,Wuhan University,Wuhan 430072,Hubei,China | 2010 | Wuhan University Journal of Natural Sciences2010，15，1： | 4 |
| 3 | 第一类导数非线性Schrdinger方程的高阶差分格式显示文摘利用Taylor展开法,给出了求解第一类导数非线性Schrdinger方程的五点四阶有限差分格式,该格式在空间上保持4阶精度,在时间上保持2阶精度。为了观察格式的适用性,将格式推广到了5阶Kd V方程。数值算例比较了该格式与Crank-Nicolson格式,验证了格式的精度阶,并给出了2个单孤子碰撞的数值模拟。 | 李书存 石方圆 | 2016 | 北京信息科技大学学报(自然科学版)2016，31，6： | 3 |
| 4 | A Newly Revised Inverse Scattering Transform for DNLS^(+) Equation under Nonvanishing Boundary Condition显示文摘A newly revised inverse scattering transform(IST) for the derivative nonlinear Schrdinger(DNLS+) equation with non-vanishing boundary condition(NVBC) and normal group velocity dispersion is proposed by introducing a suitable affine parameter in Zakharov-Shabat integral kern.The explicit breather-type one-soliton solution,which can reproduce one pure soliton at the de-generate case and one bright soliton solution at the limit of van-ishing boundary,has been derived to verify the validity of the revised IST. | ZHOU Guoquan | 2012 | Wuhan University Journal of Natural Sciences2012，17，2： | 3 |
| 5 | Explicit Breather-Type and Pure N-Soliton Solution of DNLS^+ Equation with Nonvanishing Boundary Condition显示文摘Based on a newly revised inverse scattering transform for the derivative nonlinear Schrdinger (DNLS+) equation with nonvanishing boundary condition (NVBC), the explicit breathertype and pure N-soliton solution has been derived by some algebra techniques. The two-breather solution and the pure double-soliton solution have been given as two typical examples in illustration of the general formula of the multi-soliton solution. The asymptotic behaviors of the N-soliton solution are discussed in detail. | ZHOU Guoquan | 2013 | Wuhan University Journal of Natural Sciences2013，18，2： | 3 |
| 6 | Space Periodic Solutions and Rogue Wave Solution of the Derivative Nonlinear Schrodinger Equation显示文摘The derivative nonlinear Schr?dinger equation, which is extensively applied in plasma physics and nonlinear optics, is analytically studied by Hirota method. Space periodic solutions are determined by means of Hirota's bilinear formalism, and the rogue wave solution is derived as a long-wave limit of the space periodic solution. | ZHOU Guoquan LI Xujun | 2017 | Wuhan University Journal of Natural Sciences2017，22，5： | 1 |
| 7 | Mixed Breather-Type and Pure Soliton Solution of DNLS Equation显示文摘A newly revised inverse scattering transform(IST) is used to solve the derivative nonlinear Schr?dinger(DNLS^+) equation with non-vanishing boundary condition(NVBC) and normal group-velocity dispersion, and a mixed type of soliton solution is found, which is composed of both pure and breather-type solitons. The mixed-soliton solution can degenerate into breathers and pure solitons when taking the limit of some special parameters, proving the validity of the mixed-type solution. | LI Xujun ZHOU Guoquan | 2017 | Wuhan University Journal of Natural Sciences2017，22，3： | 1 |
| 8 | 基于Hirota方法探求非零边界条件下MNLS/DNLS方程的孤子解显示文摘Hirota双线性导数变换处理非线性偏微分方程,是一种比反散射变换更为方便的直接方法。本文展示了Hirota双线性导数变换法应用于求解非线性可积方程的一般手续,以非零驻波边界条件下修正的非线性薛定谔(MNLS)方程为例,探求其孤子解;再通过简单的参数归零法直接得到导数非线性薛定谔(DNLS)方程在非零常数边界条件下的相应孤子解,亮/暗孤子解随时间和空间变量的演化也通过图像加以演示,所得孤子解与反散射方法得到的结果一致相符。 | 周国全 雒润嘉 齐蓥 | 2023 | 物理与工程2023，33，4： | 1 |
| 9 | 第一类导数非线性Schrdinger方程的时间紧致格式显示文摘利用Taylor级数展开,得到求解第一类导数非线性Schrdinger方程的时间紧致有限差分格式,该格式在空间上保持2阶精度,在时间上保持4阶精度。数值算例验证了格式的精度阶,并对2个单孤子的碰撞进行了数值模拟。 | 邵静芳 张静静 | 2017 | 北京信息科技大学学报(自然科学版)2017，32，6： | 0 |
| 10 | 第一类导数非线性Schrdinger方程的高阶紧致差分格式显示文摘利用Taylor级数展开,得到求解第一类导数非线性Schrdinger方程的五点四阶时间紧致有限差分格式,该格式在空间和时间上均保持4阶精度。数值算例验证了该格式的精度阶,并给出了2个单孤子碰撞的数值模拟。 | 邵静芳 石方圆 | 2018 | 北京信息科技大学学报(自然科学版)2018，33，1： | 0 |
| 11 | 带阻尼项的坏的Bq方程的精确解显示文摘研究求解非线性演化方程的tanh与扩展tanh函数法。使用符号计算软件maple和tanh函数法获得带阻尼项的坏的Bq方程的大量双曲函数精确解,使用符号计算软件maple和扩张tanh函数法获得带阻尼项的坏的Bq方程的大量行波精确解。 | 范凯 靳琴琴 | 2016 | 太原科技大学学报2016，37，3： | 0 |
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