HIGHER-ORDER NONLINEAR SCHRÖDINGER EQUATION IN 2D CASE
2020 Volume 72 Issue 1 Pages 15-37
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2020 Volume 72 Issue 1 Pages 15-37
We consider the Cauchy problem for the higher-order nonlinear Schrödinger equation in two dimensional case
\[ \left\{\!\!\! \begin{array}{c} i\partial _{t}u+\frac{b}{2}\Delta u-\frac{1}{4}\Delta ^{2}u=\lambda \left\vert u\right\vert u,\text{ }t>0,\text{\ }x\in \mathbb{R}^{2}\,\mathbf{,} \\
u\left ( 0,x\right) =u_{0}\left ( x\right) ,\text{\ }x\in \mathbb{R}^{2} \,\mathbf{,} \end{array} \right. \]
where $\lambda \in \mathbb{R}$, $b>0$. We develop the factorization techniques for studying the large time asymptotics of solutions to the above Cauchy problem. We prove that the asymptotics has a modified character.
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