论文标题
MKP-1,2方程的多块解决方案通过$ \ overline {\ partial} $ - 敷料
Multi-lump solutions of mKP-1,2 equations with integrable boundary condition via $\overline{\partial}$-dressing
论文作者
论文摘要
我们通过使用$ \ overline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partline \ partial $ dressing方法，构建了具有集成边界条件$ u（x，y，t）$ u（x，y，t）$ u（x，y，t）$ u（x，y，t）$ u（x，y，t）的新类别的多块解决方案的新类别。我们完全满足了$ u（x，y，t）$的现实和边界条件，并使用多个块解决方案的一般行列式公式。 We illustrated new calculated classes by simple examples of two-lump solutions and demonstrated how fulfilment of integrable boundary condition $u\big|_{y=0}=0$ via special nonlinear superposition of several single lumps leads to formation of certain eigenmodes for the field $u(x,y,t)$ in semiplane $y\geq0$, the analogs of standing waves on the string arising from corresponding boundary conditions在字符串的端点。
We constructed new classes of exact multi-lump solutions of mKP-1,2 equations with integrable boundary condition $u(x,y,t)\big|_{y=0}=0$ by the use of $\overline\partial$-dressing method of Zakharov and Manakov. We exactly satisfied reality and boundary conditions for the field $u(x,y,t)$ using general determinant formula for multi-lump solutions. We illustrated new calculated classes by simple examples of two-lump solutions and demonstrated how fulfilment of integrable boundary condition $u\big|_{y=0}=0$ via special nonlinear superposition of several single lumps leads to formation of certain eigenmodes for the field $u(x,y,t)$ in semiplane $y\geq0$, the analogs of standing waves on the string arising from corresponding boundary conditions at endpoints of string.
