TY - JOUR AU - Antonelli, P. AU - Sparber, C. PY - 2011 DA - 2011// TI - Existence of solitary waves in dipolar quantum gases JO - Physica D VL - 240 UR - https://doi.org/10.1016/j.physd.2010.10.004 DO - 10.1016/j.physd.2010.10.004 ID - Antonelli2011 ER - TY - JOUR AU - Bao, W. AU - Cai, Y. PY - 2013 DA - 2013// TI - Mathematical theory and numerical methods for Bose–Einstein condensation JO - Kinet. Relat. Models VL - 6 UR - https://doi.org/10.3934/krm.2013.6.1 DO - 10.3934/krm.2013.6.1 ID - Bao2013 ER - TY - JOUR AU - Bao, W. AU - Cai, Y. AU - Wang, H. PY - 2010 DA - 2010// TI - Efficient numerical methods for computing ground states and dynamics of dipolar Bose–Einstein condensates JO - J. Comput. Phys. VL - 229 UR - https://doi.org/10.1016/j.jcp.2010.07.001 DO - 10.1016/j.jcp.2010.07.001 ID - Bao2010 ER - TY - JOUR AU - Bellazzini, J. AU - Forcella, L. PY - 2019 DA - 2019// TI - Asymptotic dynamic for dipolar quantum gases below the ground state energy threshold JO - J. Funct. Anal. VL - 277 UR - https://doi.org/10.1016/j.jfa.2019.04.005 DO - 10.1016/j.jfa.2019.04.005 ID - Bellazzini2019 ER - TY - JOUR AU - Bellazzini, J. AU - Jeanjean, L. PY - 2016 DA - 2016// TI - On dipolar quantum gases in the unstable regime JO - SIAM J. Math. Anal. VL - 48 UR - https://doi.org/10.1137/15M1015959 DO - 10.1137/15M1015959 ID - Bellazzini2016 ER - TY - JOUR AU - Cao, J. AU - Song, G. AU - Wang, J. AU - Shi, Q. AU - Sun, S. PY - 2019 DA - 2019// TI - Blow-up and global solutions for a class of time fractional nonlinear reaction-diffusion equation with weakly spatial source JO - Appl. Math. Lett. VL - 91 UR - https://doi.org/10.1016/j.aml.2018.12.020 DO - 10.1016/j.aml.2018.12.020 ID - Cao2019 ER - TY - JOUR AU - Carles, R. AU - Hajaiej, H. PY - 2015 DA - 2015// TI - Complementary study of the standing wave solutions of the Gross–Pitaevskii equation in dipolar quantum gases JO - Bull. Lond. Math. Soc. VL - 47 UR - https://doi.org/10.1112/blms/bdv024 DO - 10.1112/blms/bdv024 ID - Carles2015 ER - TY - JOUR AU - Carles, R. AU - Markowich, P. A. AU - Sparber, C. PY - 2008 DA - 2008// TI - On the Gross–Pitaevskii equation for trapped dipolar quantum gases JO - Nonlinearity VL - 21 UR - https://doi.org/10.1088/0951-7715/21/11/006 DO - 10.1088/0951-7715/21/11/006 ID - Carles2008 ER - TY - BOOK AU - Cazenave, T. PY - 2003 DA - 2003// TI - Semilinear Schrödinger Equations PB - New York University, Courant Institute of Mathematical Sciences CY - New York ID - Cazenave2003 ER - TY - JOUR AU - Duyckaerts, T. AU - Roudenko, S. PY - 2015 DA - 2015// TI - Going beyond the threshold: scattering and blow-up in the focusing NLS equation JO - Commun. Math. Phys. VL - 344 UR - https://doi.org/10.1007/s00220-014-2202-y DO - 10.1007/s00220-014-2202-y ID - Duyckaerts2015 ER - TY - JOUR AU - Ellio, M. S. AU - Valentini, J. J. AU - Chandler, D. W. PY - 2003 DA - 2003// TI - Subkelvin cooling NO molecules via “billiard-like” collisions with argon JO - Science VL - 302 UR - https://doi.org/10.1126/science.1090679 DO - 10.1126/science.1090679 ID - Ellio2003 ER - TY - JOUR AU - Feng, B. PY - 2016 DA - 2016// TI - Sharp threshold of global existence and instability of standing wave for the Schrödinger–Hartree equation with a harmonic potential JO - Nonlinear Anal., Real World Appl. VL - 31 UR - https://doi.org/10.1016/j.nonrwa.2016.01.012 DO - 10.1016/j.nonrwa.2016.01.012 ID - Feng2016 ER - TY - JOUR AU - Feng, B. PY - 2018 DA - 2018// TI - On the blow-up solutions for the nonlinear Schrödinger equation with combined power-type nonlinearities JO - J. Evol. Equ. VL - 18 UR - https://doi.org/10.1007/s00028-017-0397-z DO - 10.1007/s00028-017-0397-z ID - Feng2018 ER - TY - JOUR AU - Feng, B. PY - 2018 DA - 2018// TI - On the blow-up solutions for the fractional nonlinear Schrödinger equation with combined power-type nonlinearities JO - Commun. Pure Appl. Anal. VL - 17 UR - https://doi.org/10.3934/cpaa.2018085 DO - 10.3934/cpaa.2018085 ID - Feng2018 ER - TY - JOUR AU - Feng, B. AU - Chen, R. AU - Wang, Q. PY - 2019 DA - 2019// TI - Instability of standing waves for the nonlinear Schrödinger–Poisson equation in the L2$L^{2}$-critical case JO - J. Dyn. Differ. Equ. UR - https://doi.org/10.1007/s10884-019-09779-6 DO - 10.1007/s10884-019-09779-6 ID - Feng2019 ER - TY - JOUR AU - Feng, B. AU - Liu, J. AU - Niu, H. AU - Zhang, B. PY - 2020 DA - 2020// TI - Strong instability of standing waves for a fourth-order nonlinear Schrödinger equation with the mixed dispersions JO - Nonlinear Anal. VL - 196 UR - https://doi.org/10.1016/j.na.2020.111791 DO - 10.1016/j.na.2020.111791 ID - Feng2020 ER - TY - JOUR AU - Gligoric, G. AU - Maluckov, A. AU - Sterpic, M. AU - Hadzievski, I. AU - Malomed, B. A. PY - 2010 DA - 2010// TI - Two dimensional discrete solutions in dipolar Bose–Einstein condensates JO - Phys. Rev. A VL - 81 UR - https://doi.org/10.1103/PhysRevA.81.013633 DO - 10.1103/PhysRevA.81.013633 ID - Gligoric2010 ER - TY - JOUR AU - Huang, J. AU - Zhang, J. PY - 2017 DA - 2017// TI - Exact value of cross-constrain problem and strong instability of standing waves in trapped dipolar quantum gases JO - Appl. Math. Lett. VL - 70 UR - https://doi.org/10.1016/j.aml.2017.03.002 DO - 10.1016/j.aml.2017.03.002 ID - Huang2017 ER - TY - JOUR AU - Lian, W. AU - Ahmed, M. AU - Xu, R. PY - 2019 DA - 2019// TI - Global existence and blow up of solution for semilinear hyperbolic equation with logarithmic nonlinearity JO - Nonlinear Anal. VL - 184 UR - https://doi.org/10.1016/j.na.2019.02.015 DO - 10.1016/j.na.2019.02.015 ID - Lian2019 ER - TY - JOUR AU - Ma, L. AU - Cao, P. PY - 2011 DA - 2011// TI - The threshold for the focusing Gross–Pitaevskii equation with trapped dipolar quantum gases JO - J. Math. Anal. Appl. VL - 381 UR - https://doi.org/10.1016/j.jmaa.2011.02.031 DO - 10.1016/j.jmaa.2011.02.031 ID - Ma2011 ER - TY - JOUR AU - Ma, L. AU - Wang, J. PY - 2013 DA - 2013// TI - Sharp threshold of the Gross–Pitaevskii equation with trapped dipolar quantum gases JO - Can. Math. Bull. VL - 56 UR - https://doi.org/10.4153/CMB-2011-181-2 DO - 10.4153/CMB-2011-181-2 ID - Ma2013 ER - TY - JOUR AU - Nath, R. AU - Pedri, P. AU - Santos, I. PY - 2007 DA - 2007// TI - Soliton-soliton scattering in dipolar Bose–Einstein condensates JO - Phys. Rev. A VL - 76 UR - https://doi.org/10.1103/PhysRevA.76.013606 DO - 10.1103/PhysRevA.76.013606 ID - Nath2007 ER - TY - JOUR AU - Pedri, P. AU - Santos, I. PY - 2005 DA - 2005// TI - Two-dimensional bright solitons in dipolar Bose–Einstein condensates JO - Phys. Rev. Lett. VL - 95 UR - https://doi.org/10.1103/PhysRevLett.95.200404 DO - 10.1103/PhysRevLett.95.200404 ID - Pedri2005 ER - TY - JOUR AU - Santos, L. AU - Shlyapnikov, G. AU - Zoller, P. AU - Lewenstein, M. PY - 2000 DA - 2000// TI - Bose–Einstein condensation in trapped dipolar gases JO - Phys. Rev. Lett. VL - 85 UR - https://doi.org/10.1103/PhysRevLett.85.1791 DO - 10.1103/PhysRevLett.85.1791 ID - Santos2000 ER - TY - JOUR AU - Shen, J. AU - Yang, Y. AU - Chen, S. AU - Xu, R. PY - 2013 DA - 2013// TI - Finite time blow up of fourth-order wave equations with nonlinear strain and source terms at high energy level JO - Int. J. Math. VL - 24 UR - https://doi.org/10.1142/S0129167X13500432 DO - 10.1142/S0129167X13500432 ID - Shen2013 ER - TY - JOUR AU - Vengalattore, M. AU - Leslie, S. R. AU - Guzman, J. AU - Stamper-Kurn, D. M. PY - 2008 DA - 2008// TI - Spontaneously modulated spin textures in a dipolar spinor Bose–Einstein condensate JO - Phys. Rev. Lett. VL - 100 UR - https://doi.org/10.1103/PhysRevLett.100.170403 DO - 10.1103/PhysRevLett.100.170403 ID - Vengalattore2008 ER - TY - JOUR AU - Xiang, M. AU - Radulescu, V. D. AU - Zhang, B. PY - 2018 DA - 2018// TI - Nonlocal Kirchhoff diffusion problems: local existence and blow-up of solutions JO - Nonlinearity VL - 31 UR - https://doi.org/10.1088/1361-6544/aaba35 DO - 10.1088/1361-6544/aaba35 ID - Xiang2018 ER - TY - JOUR AU - Xie, Y. AU - Li, L. AU - Zhu, S. PY - 2018 DA - 2018// TI - Dynamical behaviors of blowup solutions in trapped quantum gases: concentration phenomenon JO - J. Math. Anal. Appl. VL - 468 UR - https://doi.org/10.1016/j.jmaa.2018.08.011 DO - 10.1016/j.jmaa.2018.08.011 ID - Xie2018 ER - TY - JOUR AU - Xu, R. AU - Su, J. PY - 2013 DA - 2013// TI - Global existence and finite time blow-up for a class of semilinear pseudo-parabolic equations JO - J. Funct. Anal. VL - 264 UR - https://doi.org/10.1016/j.jfa.2013.03.010 DO - 10.1016/j.jfa.2013.03.010 ID - Xu2013 ER - TY - JOUR AU - Xu, R. AU - Wang, X. AU - Yang, Y. PY - 2018 DA - 2018// TI - Blowup and blowup time for a class of semilinear pseudo-parabolic equations with high initial energy JO - Appl. Math. Lett. VL - 83 UR - https://doi.org/10.1016/j.aml.2018.03.033 DO - 10.1016/j.aml.2018.03.033 ID - Xu2018 ER - TY - JOUR AU - Xu, R. AU - Wang, X. AU - Yang, Y. AU - Chen, S. PY - 2018 DA - 2018// TI - Global solutions and finite time blow-up for fourth order nonlinear damped wave equation JO - J. Math. Phys. VL - 59 UR - https://doi.org/10.1063/1.5006728 DO - 10.1063/1.5006728 ID - Xu2018 ER - TY - JOUR AU - Yang, L. AU - Li, X. AU - Wu, Y. AU - Caccetta, L. PY - 2017 DA - 2017// TI - Global well-posedness and blow-up for the Hartree equation JO - Acta Math. Sci. Ser. B Engl. Ed. VL - 37 UR - https://doi.org/10.1016/S0252-9602(17)30049-8 DO - 10.1016/S0252-9602(17)30049-8 ID - Yang2017 ER - TY - JOUR AU - Yang, Y. AU - Xu, R. PY - 2018 DA - 2018// TI - Finite time blowup for nonlinear Klein–Gordon equations with arbitrarily positive initial energy JO - Appl. Math. Lett. VL - 77 UR - https://doi.org/10.1016/j.aml.2017.09.014 DO - 10.1016/j.aml.2017.09.014 ID - Yang2018 ER - TY - JOUR AU - Yang, Y. AU - Xu, R. PY - 2019 DA - 2019// TI - Nonlinear wave equation with both strongly and weakly damped terms: supercritical initial energy finite time blow up JO - Commun. Pure Appl. Anal. VL - 18 UR - https://doi.org/10.3934/cpaa.2019065 DO - 10.3934/cpaa.2019065 ID - Yang2019 ER - TY - JOUR AU - Yi, S. AU - You, L. PY - 2000 DA - 2000// TI - Trapped atomic condensates with anisotropic interactions JO - Phys. Rev. A VL - 61 UR - https://doi.org/10.1103/PhysRevA.61.041604 DO - 10.1103/PhysRevA.61.041604 ID - Yi2000 ER - TY - JOUR AU - Yue, Z. AU - Li, X. AU - Zhang, J. PY - 2016 DA - 2016// TI - A new blow-up criterion for Gross–Pitaevskii equation JO - Appl. Math. Lett. VL - 62 UR - https://doi.org/10.1016/j.aml.2016.06.007 DO - 10.1016/j.aml.2016.06.007 ID - Yue2016 ER - TY - JOUR AU - Zhang, J. PY - 2002 DA - 2002// TI - Sharp conditions of global existence for nonlinear Schrödinger and Klein–Gordon equations JO - Nonlinear Anal. VL - 48 UR - https://doi.org/10.1016/S0362-546X(00)00180-2 DO - 10.1016/S0362-546X(00)00180-2 ID - Zhang2002 ER - TY - JOUR AU - Zhang, J. PY - 2005 DA - 2005// TI - Sharp threshold for blowup and global existence in nonlinear Schrödinger equations under a harmonic potential JO - Commun. Partial Differ. Equ. VL - 30 UR - https://doi.org/10.1080/03605300500299539 DO - 10.1080/03605300500299539 ID - Zhang2005 ER - TY - JOUR AU - Zhang, J. AU - Zhu, S. PY - 2011 DA - 2011// TI - Sharp blow-up criteria for the Davey–Stewartson system in R3$\mathbb{R}^{3}$ JO - Dyn. Partial Differ. Equ. VL - 8 UR - https://doi.org/10.4310/DPDE.2011.v8.n3.a4 DO - 10.4310/DPDE.2011.v8.n3.a4 ID - Zhang2011 ER - TY - JOUR AU - Zhang, J. AU - Zhu, S. PY - 2019 DA - 2019// TI - Sharp energy criteria and singularity of blow-up solutions for the Davey–Stewartson system JO - Commun. Math. Sci. VL - 17 UR - https://doi.org/10.4310/CMS.2019.v17.n3.a4 DO - 10.4310/CMS.2019.v17.n3.a4 ID - Zhang2019 ER - TY - JOUR AU - Zhu, S. PY - 2016 DA - 2016// TI - On the Davey–Stewartson system with competing nonlinearities JO - J. Math. Phys. VL - 57 UR - https://doi.org/10.1063/1.4942633 DO - 10.1063/1.4942633 ID - Zhu2016 ER -