当前位置: X-MOL 学术Phys. D Nonlinear Phenom. › 论文详情
Our official English website, www.x-mol.net, welcomes your feedback! (Note: you will need to create a separate account there.)
Multi-lump solutions of KP equation with integrable boundary via ∂¯-dressing method
Physica D: Nonlinear Phenomena ( IF 4 ) Pub Date : 2020-09-21 , DOI: 10.1016/j.physd.2020.132740
V.G. Dubrovsky , A.V. Topovsky

We constructed new classes of exact multi-lump solutions of KP-1 and KP-2 versions of KP equations with integrable boundary condition uy|y=0=0 by the use of ¯-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 can be exactly satisfied in the framework of ¯-dressing method. 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 y0 as analogs of standing waves on a string with fixed end points.



中文翻译:

具有可积边界的KP方程的多集解 ¯着装方法

我们构造了具有可积边界条件的KP方程的KP-1和KP-2版本的新型精确多体解 üÿ|ÿ=0=0 通过使用 ¯扎克罗夫和马纳科夫的选址方法,并推导了此类解的一般行列式。我们展示了该领域的现实和边界条件ü 可以完全满足以下条件 ¯-装扮方法。在这里,我们给出具有可积边界的两集解的显式示例,作为两个更简单的变形一集解的非线性叠加:满足边界条件会导致形成某些本征üXÿŤ 在半平面 ÿ0 作为具有固定端点的弦上驻波的类似物。

更新日期:2020-09-21
down
wechat
bug