论文标题
具有立方体和四分之一非线性的延长非线性schrödinger方程的高阶光滑正面和呼吸声音解决方案
Higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity
论文作者
论文摘要
我们构建了具有以立方和四分之一非线性的扩展非线性schrödinger方程的某些高阶光滑正面和呼吸声溶液。我们利用广义的Darboux转换方法来构建上述解决方案。三个众所周知的方程，即非线性schrödinger方程，hirota方程和广义的非线性schrödinger方程，是被认为是扩展的非线性schrödinger方程的子基数。我们构建的解决方案更为笼统。我们分析了组成方程的正值和呼吸额度解决方案如何通过高阶非线性和分散项来修改。我们的结果表明，光滑的座子和呼吸 - 波西顿溶液的宽度和方向对高阶效应高度敏感。此外，我们进行了渐近分析以预测正电子的行为。我们观察到在碰撞期间表现出时间依赖性相位移位。我们还介绍了正面的时间依赖性相位移位的确切表达。最后，我们表明，这种时间相关的相移与高阶非线性和分散参数成正比。
We construct certain higher order smooth positon and breather positon solutions of an extended nonlinear Schrödinger equation with the cubic and quartic nonlinearity. We utilize the generalized Darboux transformation method to construct the aforementioned solutions. The three well-known equations, namely nonlinear Schrödinger equation, Hirota equation, and generalized nonlinear Schrödinger equation, are sub-cases of the considered extended nonlinear Schrödinger equation. The solutions which we construct are more general. We analyze how the positon and breather positon solutions of the constituent equations get modified by the higher order nonlinear and dispersion terms. Our results show that the width and direction of the smooth positon and breather-positon solutions are highly sensitive to higher-order effects. Further, we carryout an asymptotic analysis to predict the behaviour of positons. We observe that during collision positons exhibit a time-dependent phase shift. We also present the exact expression of time-dependent phase shift of positons. Finally, we show that this time-dependent phase shift is directly proportional to the higher order nonlinear and dispersion parameters.
