Uniqueness and structure-preserving numerical simulations for an Ultrahyperbolic Schrödinger equation
Ozlem Kaytmaz, Muhammed Hasdemir
article (Uluslararası, Hakemli) | Yazar(lar): Ozlem Kaytmaz, Muhammed Hasdemir | Yıl: 2026 — Özet: In this paper, we investigate a Cauchy problem for an ultrahyperbolic Schr & ouml;dinger equation posed in an unbounded domain. Ultrahyperbolic Schr & ouml;dinger models arise in multidimensional wave propagation and have
In this paper, we investigate a Cauchy problem for an ultrahyperbolic Schr & ouml;dinger equation posed in an unbounded domain. Ultrahyperbolic Schr & ouml;dinger models arise in multidimensional wave propagation and have applications in water wave theory, quantum kinetic theory, ferromagnetism, nonlinear optics, and plasma physics. A uniqueness result for the considered Cauchy problem is established using a pointwise Carleman estimate. In addition, a second-order, structure-preserving Crank-Nicolson finite-difference scheme is developed for the numerical solution of the problem. For the homogeneous constant-coefficient problem, its discrete evolution is unitary and conserves the discrete -norm exactly. Numerical experiments illustrate the behaviour of solutions and verify the accuracy and conservation properties of the numerical scheme.