2003/11/09 by Jens Hoppe, Ari Laptev, Hoppe, Jens +5
Mathematics · Physics and Astronomy · #34L30 (Secondary) #34L40 (Primary) #Algebraic and Geometric Analysis #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Numerical methods for differential equations #Spectral Theory (math.SP) #Spectral Theory in Mathematical Physics #math-ph #math.MP #math.SP #msc:34L30 #msc:34L40
paper · pdf · doi:10.48550/arxiv.math-ph/0311011
11 pages
arxiv created 2003/11/09 · openalex publication_date 2003/11/09 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
A non-linear functional Q[u,v] is given that governs the loss, respectively gain, of (doubly degenerate) eigenvalues of fourth order differential operators L = ∂4 + ∂ u ∂ + v on the line. Apart from factorizing L as A*A + E0, providing several explicit examples, and deriving various relations between u, v and eigenfunctions of L, we find u and v such that L is isospectral to the free operator L0 = ∂4 up to one (multiplicity 2) eigenvalue E0 < 0. Not unexpectedly, this choice of u, v leads to exact solutions of the corresponding time-dependent PDE's.