We consider the Cauchy problem of integrable nonlinear Schrödinger equation with quartic terms on the line. The first part of the paper considers the Riemann-Hilbert formula via the unified method(also known as the Fokas method). The second part of the paper establishes asymptotic formulas for the solution of initial value problem using the nonlinear steepest descent method(also known as the Deift-Zhou method).

中文翻译：

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具有四次项的可积非线性薛定谔方程的渐近行为：柯西问题

我们考虑具有四次项的可积非线性薛定谔方程的柯西问题。论文的第一部分通过统一方法（也称为Fokas方法）考虑了Riemann-Hilbert公式。论文的第二部分建立了使用非线性最速下降法（也称为Deift-Zhou 法）求解初值问题的渐近公式。