This work proposes the numerical solutions of the cubic nonlinear Schrödinger equation subjected to rational initial value for three cases, (i) Akhmediev breather (ii) Peregrine and (iii) Kuznetsov-Ma solitons by operating exponential time differencing method (ETDM). The work shows that ETDM is a reliable and accurate method to find the solutions comparing to Adomian decomposition method (ADM) and Laplace-Adomian decomposition method (LADM).

中文翻译：

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指数时差法分析光纤中的呼吸和孤子波

这项工作提出了三种情况下的三次非线性Schrödinger方程在有理初始值的情况下的数值解：（i）Akhmediev通气（ii）百富勤和（iii）Kuznetsov-Ma孤子通过使用指数时差方法（ETDM）。这项工作表明，与Adomian分解方法（ADM）和Laplace-Adomian分解方法（LADM）相比，ETDM是一种可靠，准确的解决方案。