References
- Feynman RP, Leighton RB, Sands M. The Feynman lectures on physics, Vol. III. Addison-Wesley: Reading, MA.1965.
- Herzberg G. Spectra of diatomic molecules. New York: Van Nostrand Reinhold; 1950.
- Schrödinger E. An undulatory theory of the mechanics of atoms and molecules. Phys Rev. 1926;28(6):1049–1070. doi: https://doi.org/10.1103/PhysRev.28.1049
- Davey A, Stewartson K. On three-dimensional packets of surface waves. Proc R Soc Lond A Math Phys Eng Sci. 1974;338(1613):101–110.
- Djordjevic VD, Redekopp LG. On two-dimensional packets of capillary-gravity waves. J Fluid Mech. 1977;79(4):703–714. doi: https://doi.org/10.1017/S0022112077000408
- Ichinose W. A note on the Cauchy problem for Schrödinger type equations on the Riemannian manifold. Math Japon. 1990;35:205–213.
- Zakharov VE, Kuznetsov EA. Multi-scale expansions in the theory of systems integrable by the inverse scattering transform. Phys D. 1986;18(1–3):455–463. doi: https://doi.org/10.1016/0167-2789(86)90214-9
- Zakharov VE, Schulman EI. Degenerative dispersion laws, motion invariants and kinetic equations. Phys D. 1980;1(2):192–202. doi: https://doi.org/10.1016/0167-2789(80)90011-1
- Ablowitz MJ, Haberman R. Nonlinear evolution equations in two and three dimensions. Phys Rev Lett. 1975;35(18):1185–1188. doi: https://doi.org/10.1103/PhysRevLett.35.1185
- Konopelchenko BG, Matkarimov BT. On the inverse scattering transform for the Ishimori equation. Phys Lett A. 1989;135(3):183–189. doi: https://doi.org/10.1016/0375-9601(89)90259-4
- Amirov AK. Integral geometry and inverse problems for kinetic equations. VSP: Utrecht; 2001.
- Sulem C, Sulem PL. The nonlinear Schrödinger equation: self-focusing and wave collapse. Springer; 1999.
- Kenig CE, Ponce G, Vega L. Smoothing effects and local existence theory for the generalized nonlinear Schrödinger equations. Invent Math. 1998;134(3):489–545. doi: https://doi.org/10.1007/s002220050272
- Kenig CE, Ponce G, Rolvung C, et al. The general quasilinear ultrahyperbolic Schrödinger equation. Adv Math. 2006;206(2):402–433. doi: https://doi.org/10.1016/j.aim.2005.09.005
- Isakov V. Inverse problems for partial differential equations. New York: Springer; 2006.
- Carleman T. Sur un probleme, d'unicité pour les systemes d'équations aux derivées partiellesa deux variables independentes. Ark Mat Astr Fys. 1939;2:1–9.
- Kenig CE. Carleman estimates, uniform Sobolev inequalities for second-order differential operators, and unique continuation theorems. Proc Int Congr Math. 1986;1:948–960.
- Calderón AP. Uniqueness in the Cauchy problem for partial differential equations. Am J Math. 1958;80(1):16–36. doi: https://doi.org/10.2307/2372819
- Hörmander L. Linear partial differential operators. New York: Springer; 1963.
- Amirov AK, Yamamoto M. Unique continuation and an inverse problem for hyperbolic equations across a general hypersurface. J Phys Conf Ser. 2005;12:1–12. doi: https://doi.org/10.1088/1742-6596/12/1/001
- Yamamoto M. Carleman estimates for parabolic equations and applications. Inverse Probl. 2009;25(12):123013. doi: https://doi.org/10.1088/0266-5611/25/12/123013
- Isakov V, Kim N. Carleman estimates with two large parameters for second order operators and applications to elasticity with residual stress. Appl Math. 2008;4(35):447–465.
- Gölgeleyen F, Yamamoto M. Stability of inverse problems for ultrahyperbolic equations. Chin Ann Math B. 2014;35(4):527–556. doi: https://doi.org/10.1007/s11401-014-0848-6
- Gölgeleyen F, Yamamoto M. Uniqueness of solution of an inverse source problem for ultrahyperbolic equations. Inverse Probl. 2020;36(3):035008. doi: https://doi.org/10.1088/1361-6420/ab63a2
- Gölgeleyen F, Kaytmaz Ö. A Hölder stability estimate for inverse problems for the ultrahyperbolic Schrödinger equation. Anal Math Phys. 2019;9(4):2171–2199. doi: https://doi.org/10.1007/s13324-019-00326-6
- Baudouin L, Yamamoto M. Inverse problem on a tree-shaped network: unified approach for uniqueness. Appl Anal. 2015;94(11):2370–2395. doi: https://doi.org/10.1080/00036811.2014.985214
- Yuan G, Yamamoto M. Carleman estimates for the Schrödinger equation and applications to an inverse problem and an observability inequality. Chin Ann Math B. 2010;31(4):555–578. doi: https://doi.org/10.1007/s11401-010-0585-4
- Lions JL, Magenes E. Non-Homogeneous boundary value problems and applications. Berlin: Springer; 1972.
- Craig W, Weinstein S. On determinism and well-posedness in multiple time dimensions. Proc R Soc A. 2009;465:3023–3046. doi: https://doi.org/10.1098/rspa.2009.0097
- Tegmark M. On the dimensionality of spacetime. Class Quant Grav. 1997;14(4):L69–L75. doi: https://doi.org/10.1088/0264-9381/14/4/002