论文标题
在表面等离子体极性的双线非线性问题中，特征值分叉
Eigenvalue Bifurcation in Doubly Nonlinear Problems with an Application to Surface Plasmon Polaritons
论文作者
论文摘要
我们考虑一类通常在解决方案和特征值参数（“双重”非线性）中非线性的一类通常的非自助特征值问题。我们证明了使用Lyapunov-Schmidt还原的线性问题的简单隔离特征值引起的分叉，并提供了非线性特征值和溶液的扩展。我们进一步证明，如果线性特征值是真实的，并且非线性问题$ \ MATHCAL P \ MATHCAL T $ - 对称，则分叉非线性特征值仍然是真实的。然后将这些一般结果应用于表面等离子体极化子（SPP）的背景下，即在介电和金属层之间存在一个或多个接口的情况下，非线性麦克斯韦方程的局部溶液。我们在某些$ \ MATHCAL P \ MATHCAL t $ -smmetric配置中获得了横向电spps的存在。
We consider a class of generally non-self-adjoint eigenvalue problems which are nonlinear in the solution as well as in the eigenvalue parameter ("doubly" nonlinear). We prove a bifurcation result from simple isolated eigenvalues of the linear problem using a Lyapunov-Schmidt reduction and provide an expansion of both the nonlinear eigenvalue and the solution. We further prove that if the linear eigenvalue is real and the nonlinear problem $\mathcal P\mathcal T$-symmetric, then the bifurcating nonlinear eigenvalue remains real. These general results are then applied in the context of surface plasmon polaritons (SPPs), i.e. localized solutions for the nonlinear Maxwell's equations in the presence of one or more interfaces between dielectric and metal layers. We obtain the existence of transverse electric SPPs in certain $\mathcal P\mathcal T$-symmetric configurations.
