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 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 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 in semiplane 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 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 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场 在半平面 作为具有固定端点的弦上驻波的类似物。