论文标题
MKP-1方程的新的确切定期解决方案通过$ \叠加{\ partial} $ - 敷料
New exact periodical solutions of mKP-1 equation via $\overline{\partial}$-dressing
论文作者
论文摘要
我们提出了通过Zakharov-Manakov $ \ OPERLINE {\ partial} $ - 敷料方法来构建MKP-1方程的精确定期解决方案的一般计划。我们计算了MKP-1方程的新的精确周期溶液：1。非挥发性溶液或非线性平面单色波的类别； 2。两期溶液的类别，没有任何边界条件； 3。具有集成边界条件$ u（x，y，t）\ mid_ {y = 0} = 0 $的两个周期解决方案的类别。我们解释了三个周期解决方案的第三类，其通过使用特殊的非线性叠加来获得的集成边界条件，将两个简单的单次波浪的特殊非线性叠加用作场上$ u（x，y，y，t）$ in emi-plane $ y \ y \ e fegq 0 $的字段$ u（x，x，y，t）$的特征振荡的类似物，该字符串与固定的Endoints的字符串相似。
We proposed general scheme for construction of exact real periodical solutions of mKP-1 equation via Zakharov-Manakov $\overline{\partial}$-dressing method, derived convenient determinant formula for calculation of such solutions and demonstrated how reality and boundary conditions for the field $u(x,y,t)$ can be satisfied. We calculated the new classes of exact periodical solutions of mKP-1 equation: 1. the class of nonsingular one-periodic solutions or nonlinear plane monochromatic waves; 2. the class of two-periodic solutions without imposition of any boundary condition; 3. the class of two-periodic solutions with integrable boundary condition $u(x,y,t)\mid_{y=0}=0$. We interpreted the third class of two-periodic solutions with integrable boundary condition obtained by the use of special nonlinear superpositions of two simple one-periodical waves as eigenmodes of oscillations of the field $u(x,y,t)$ in semi-plane $y\geq 0$, the analogs of standing waves on the string with fixed endpoints.
