论文标题
通过$ \ overline \ partial $ dressing方法，具有集成边界的KP方程的多 - 固体解决方案
Multi-soliton solutions of KP equation with integrable boundary via $\overline\partial$-dressing method
论文作者
论文摘要
KADOMTSEV-PETVIASHVILI方程的KP-1和KP-2版本的新型多苏利顿解决方案具有可集成的边界条件$ u_ {y} \ big | _ {y = 0} = 0 $，通过使用$ \ overline \ overline \ oftline \ partline \ partial $ drespial $ dressial $ dressial $ dressial $ dressial-dressial-dressiged。得出了这种解决方案的方便形式的一般决定因素公式。它显示了在$ \ overline \ partial $ dressing方法的框架中如何完全满足$ u（x，y，t）$的现实和边界条件。两种溶解解决方案的明确示例是两个更简单的非线性叠加，“变形” \，单溶解质量为插图：边界条件的实现会导致形成两个更简单的单solitons的界限，从而形成了更简单的单solitons，并与$ u（x，y，y y-ege y y y y-egenmodes $ y y-y-yi-plem y y y-y-yi-i-plem y y-y-yi-i-plem y y-y-y-y-y-i-plples y y y y y y y y y y y，带有固定端点的字符串。
New classes of exact multi-soliton solutions of KP-1 and KP-2 versions of Kadomtsev-Petviashvili equation with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov are constructed in the paper. General determinant formula in convenient form for such solutions is derived. It is shown how reality and boundary conditions for the field $u(x,y,t)$ in the framework of $\overline\partial$-dressing method can be satisfied exactly. Explicit examples of two-soliton solutions as nonlinear superpositions of two more simpler \,"deformed"\, one-solitons are presented as illustrations: the fulfillment of boundary condition leads to formation of bound state of two more simpler one-solitons, resonating eigenmodes of $u(x,y,t)$ in semi-plane $y\geq0$ as analogs of standing waves on the string with fixed end points.
