Guillaume Rialland
Via a fixed point argument, we construct solitary waves for the two-dimensional Zakharov system that travel with any small speed $c \in \mathbb{R}^2$. Moreover, we investigate their asymptotic behavior.
Guillaume Rialland
This paper contains 2 sections, 7 theorems, 85 equations.
Theorem 1
There exists $c_* \in (0 \, , 1)$ such that, for any $c \in \mathbb{R}^2$ with $|c| < c_*$, there exist $(U_c \, , N_c \, , V_c) \in H^1 ( \mathbb{R}^2 \, , \mathbb{C} ) \times L^2 ( \mathbb{R}^2 \, , \mathbb{R} ) \times L^2 ( \mathbb{R}^2 \, , \mathbb{R}^2 )$ such that, for any $\omega >0$, the fun Moreover, for any $m \in \mathbb{N}^2$, and $|y| \geqslant 1$,
