We consider the semilinear wave equation with power nonlinearity in one spacedimension. Given a blow-up solution with a characteristic point, we refine theblow-up behavior first derived by Merle and Zaag. We also refine the geometryof the blow-up set near a characteristic point, and show that except may be forone exceptional situation, it is never symmetric with the respect to thecharacteristic point. Then, we show that all blow-up modalities predicted bythose authors do occur. More precisely, given any integer $k\ge 2$ and $\zeta_0\in \m R$, we construct a blow-up solution with a characteristic point $a$,such that the asymptotic behavior of the solution near $(a,T(a))$ shows adecoupled sum of $k$ solitons with alternate signs, whose centers (in thehyperbolic geometry) have $\zeta_0$ as a center of mass, for all times.
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机译：我们考虑在一维空间中具有功率非线性的半线性波动方程。在给定具有特征点的爆破解决方案的情况下，我们优化了首先由Merle和Zaag推导的爆破行为。我们还对特征点附近爆破集的几何形状进行了细化，并表明，除了可能出现的一种特殊情况外，它从未相对于特征点对称。然后，我们证明了这些作者所预测的所有爆炸模式都发生了。更准确地说，给定\ m R $中的任何整数$ k \ ge 2 $和$ \ zeta_0 \，我们构造一个特征点为$ a $的爆破解，使得该解的渐近行为接近$（a ，T（a））$表示具有替换符号的$ k $孤子的耦合总和，其中心（在双曲线几何中）始终以$ \ zeta_0 $作为质心。
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