论文标题
通过$ \ overline \ partial $ dressing方法，具有集成边界的KP方程的多块解决方案
Multi-lump solutions of KP equation with integrable boundary via $\overline\partial$-dressing method
论文作者
论文摘要
我们构建了具有集成边界条件的KP-1和KP-2版本的新类别的多块解决方案，该方程$ u_ {y} \ big | _ {y = 0} = 0 $，通过使用$ \ overline \ overline \ partial \ partial $ drespial $ - Zakharov和Manakov和Manakov和Derives derives Solutions Solutions的Solutions solutions solutions solutions。我们展示了在$ \ overline \ partial $ dressing方法的框架中，现场$ u $的现实和边界条件如何完全满足。 Here we present explicit examples of two-lump solutions with integrable boundary as nonlinear superpositions of two more simpler "deformed" one-lump solutions: the fulfillment of boundary condition leads to formation of certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of standing waves on string with fixed end points.
We constructed the new classes of exact multi-lump solutions of KP-1 and KP-2 versions of KP equations with integrable boundary condition $u_{y}\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov and derived general determinant formula for such solutions. We demonstrated how reality and boundary conditions for the field $u$ in the framework of $\overline\partial$-dressing method can be exactly satisfied. Here we present explicit examples of two-lump solutions with integrable boundary as nonlinear superpositions of two more simpler "deformed" one-lump solutions: the fulfillment of boundary condition leads to formation of certain eigenmodes of the field $u(x,y,t)$ in semiplane $y\geq 0$ as analogs of standing waves on string with fixed end points.
