A New Approach for Numerically Solving Nonlinear Eigensolution Problems Academic Article

abstract

• 2014, Springer Science+Business Media New York. By considering a constraint on the energy profile, a new implicit approach is developed to solve nonlinear eigensolution problems. A corresponding minimax method is modified to numerically find eigensolutions in the order of their eigenvalues to a class of semilinear elliptic eigensolution problems from nonlinear optics and other nonlinear dispersive/diffusion systems. It turns out that the constraint is equivalent to a constraint on the wave intensity in L-(p+1) norm. The new approach enables people to establish some interesting new properties, such as wave intensity preserving/control, bifurcation identification, etc., and to explore their applications. Numerical results are presented to illustrate the method.

authors

• Zhou, Jianxin

published proceedings

• Journal of Scientific Computing

author list (cited authors)

• Wang, C., & Zhou, J.

citation count

• 1

complete list of authors

• Wang, Changchun||Zhou, Jianxin

publication date

• July 2015

publisher

• Springer Nature  Publisher

published in

• Journal of Scientific Computing  Journal

keywords

• 49 Mathematical Sciences
• 4901 Applied Mathematics
• 4903 Numerical And Computational Mathematics

Digital Object Identifier (DOI)

• 10.1007/s10915-014-9925-y

start page

• 109

end page

• 129

volume

• 64

issue

• 1

URL

• http://dx.doi.org/10.1007/s10915-014-9925-y