标题： 标量行为对于半线性波动方程爆破解中出现的复多孤子 显示英文标题

标题： Scalar behavior for a complex multi-soliton arising in blow-up for a semilinear wave equation

摘要： 本文研究了维度1中的复值半线性波动方程的爆破解，该方程具有幂非线性。 在解在复平面上旋转的情况下，我们证明在特征爆破点附近，解的行为与实值情况完全相同。 即，经过复平面上的旋转后，解可以分解为有限个具有交替符号的解耦孤立子之和。 我们证明的主要创新之处在于解决了控制孤立子位置和相位演化的复值一阶Toda系统。 显示英文摘要

摘要： This paper deals with blow-up for the complex-valued semilinear wave equation with power nonlinearity in dimension 1. Up to a rotation of the solution in the complex plane, we show that near a characteristic blow-up point, the solution behaves exactly as in the real-valued case. Namely, up to a rotation in the complex plane, the solution decomposes into a sum of a finite number of decoupled solitons with alternate signs. The main novelty of our proof is a resolution of a complex-valued first order Toda system governing the evolution of the positions and the phases of the solitons.