Li, Hang; Su, Chunmei Low-regularity exponential-type integrators for the Zakharov system with rough data in all dimensions. (English) Zbl 07962051 Math. Comput. 94, No. 352, 727-762 (2025). MSC: 65M70 65T50 65N35 65M12 65M15 35B65 35C08 35Q53 × Cite Format Result Cite Review PDF Full Text: DOI
Guo, Yuli; Zhang, Weiguo; Li, Xiang Exact periodic wave solutions of the cubic-quintic Zakharov equation and their evolution with Hamilton energy. (English) Zbl 1534.35060 J. Phys. A, Math. Theor. 57, No. 6, Article ID 065205, 46 p. (2024). MSC: 35C05 35C07 35C08 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Herr, Sebastian; Kato, Isao; Kinoshita, Shinya; Spitz, Martin Local well-posedness of a system describing laser-plasma interactions. (English) Zbl 1530.35279 Vietnam J. Math. 51, No. 4, 759-770 (2023). MSC: 35Q55 35L70 35B30 35A01 35A02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Kinoshita, Shinya; Nakamura, Shohei; Sanwal, Akansha Decoupling inequality for paraboloid under shell type restriction and its application to the periodic Zakharov system. (English) Zbl 1528.35148 Commun. Math. Phys. 404, No. 2, 883-926 (2023). MSC: 35Q53 35Q55 35B65 35A01 35A02 82D10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Candy, Timothy; Herr, Sebastian; Nakanishi, Kenji The Zakharov system in dimension \(d \geq 4\). (English) Zbl 1519.35284 J. Eur. Math. Soc. (JEMS) 25, No. 8, 3177-3228 (2023). MSC: 35Q55 35Q41 42B37 35L70 35P25 35A01 35A02 35B65 35B30 35B05 82D10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Choi, Brian Remark on the adiabatic limit of quantum Zakharov system. (English) Zbl 1504.35416 Bull. Malays. Math. Sci. Soc. (2) 45, No. 4, 1711-1735 (2022). MSC: 35Q40 35Q55 35Q41 81Q80 35B30 35B65 35A01 35A02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ozawa, Tohru; Tomioka, Kenta Schrödinger-improved Boussinesq system in two space dimensions. (English) Zbl 1490.35439 J. Evol. Equ. 22, No. 2, Paper No. 35, 16 p. (2022). MSC: 35Q55 35Q41 35Q53 35A35 35B30 35L70 35D35 35A01 35A02 76Q05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Sanwal, Akansha Local well-posedness for the Zakharov system in dimension \(d \leqslant 3\). (English) Zbl 1483.35225 Discrete Contin. Dyn. Syst. 42, No. 3, 1067-1103 (2022). MSC: 35Q55 35A01 35A02 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Ozawa, Tohru; Tomioka, Kenta Zakharov system in two space dimensions. (English) Zbl 1478.35195 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 214, Article ID 112532, 20 p. (2022). Reviewer: Anthony D. Osborne (Keele) MSC: 35Q55 35A35 35B30 35A01 35A02 35L70 82D10 × Cite Format Result Cite Review PDF Full Text: DOI
Martínez, María E. On the decay problem for the Zakharov and Klein-Gordon-Zakharov systems in one dimension. (English) Zbl 1481.35064 J. Evol. Equ. 21, No. 4, 3733-3763 (2021). MSC: 35B40 35G55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Schneider, Guido The Zakharov limit of Klein-Gordon-Zakharov like systems in case of analytic solutions. (English) Zbl 1475.35025 Appl. Anal. 100, No. 12, 2659-2667 (2021). MSC: 35B25 35L51 × Cite Format Result Cite Review PDF Full Text: DOI
Wu, Xinglong; Guo, Boling Qualitative analysis of solutions for the generalized Zakharov equations with magnetic field in \(\mathbb{R}^d\). (English) Zbl 1470.35342 Indiana Univ. Math. J. 70, No. 1, 49-79 (2021). MSC: 35Q55 35B40 35B44 35A01 35A02 82D10 76W05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Baumstark, Simon; Schratz, Katharina Asymptotic preserving trigonometric integrators for the quantum Zakharov system. (English) Zbl 1466.65162 BIT 61, No. 1, 61-81 (2021). MSC: 65M99 65N35 65M15 65M12 81Q80 35Q40 × Cite Format Result Cite Review PDF Full Text: DOI Link
Colin, Mathieu; Watanabe, Tatsuya Cauchy problem for the nonlinear Schrödinger equation coupled with the Maxwell equation. (Problème de Cauchy pour une équation de Schrödinger nonlinéaire couplée avec les équations de Maxwell.) (English. French summary) Zbl 1483.35203 Ann. Henri Lebesgue 3, 67-85 (2020). MSC: 35Q55 35L45 35L70 35Q61 × Cite Format Result Cite Review PDF Full Text: DOI
Baumstark, Simon; Schneider, Guido; Schratz, Katharina; Zimmermann, Dominik Effective slow dynamics models for a class of dispersive systems. (English) Zbl 1452.35014 J. Dyn. Differ. Equations 32, No. 4, 1867-1899 (2020). MSC: 35B25 35K90 35L90 35L10 × Cite Format Result Cite Review PDF Full Text: DOI Link
Fan, Jishan; Ozawa, Tohru Cauchy problem and vanishing dispersion limit for Schrödinger-improved Boussinesq equations. (English) Zbl 1433.35361 J. Math. Anal. Appl. 485, No. 2, Article ID 123857, 7 p. (2020). MSC: 35Q55 35B30 35L72 × Cite Format Result Cite Review PDF Full Text: DOI
Fang, Yung-Fu; Kuo, Hung-Wen; Shih, Hsi-Wei; Wang, Kuan-Hsiang Semi-classical limit for the Quantum Zakharov system. (English) Zbl 1421.35302 Taiwanese J. Math. 23, No. 4, 925-949 (2019). MSC: 35Q40 35L30 35L05 35Q55 81Q80 × Cite Format Result Cite Review PDF Full Text: DOI Euclid
Fang, Yung-Fu; Nakanishi, Kenji Global well-posedness and scattering for the quantum Zakharov system in \(L^2\). (English) Zbl 1420.35352 Proc. Am. Math. Soc., Ser. B 6, 21-32 (2019). MSC: 35Q55 35L30 35L05 35A01 35A02 × Cite Format Result Cite Review PDF Full Text: DOI
Baumstark, Simon; Schratz, Katharina Uniformly accurate oscillatory integrators for the Klein-Gordon-Zakharov system from low- to high-plasma frequency regimes. (English) Zbl 1441.76086 SIAM J. Numer. Anal. 57, No. 1, 429-457 (2019). Reviewer: Vanja Nikolić (Nijmegen) MSC: 76M22 35C20 35Q55 65M06 65M12 65M15 65M70 76X05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luong, Hung Local well-posedness for the Zakharov system on the background of a line soliton. (English) Zbl 1397.35217 Commun. Pure Appl. Anal. 17, No. 6, 2657-2682 (2018). MSC: 35Q35 35Q55 35B35 35C08 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Luong, Hung; Mauser, Norbert J.; Saut, Jean-Claude On the Cauchy problem for the Zakharov-Rubenchik/Benney-Roskes system. (English) Zbl 1397.35218 Commun. Pure Appl. Anal. 17, No. 4, 1573-1594 (2018). MSC: 35Q35 35Q55 35C08 35B35 76B15 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gauckler, Ludwig On a splitting method for the Zakharov system. (English) Zbl 1397.65166 Numer. Math. 139, No. 2, 349-379 (2018). Reviewer: Charis Harley (Johannesburg) MSC: 65M15 65P10 65M20 35Q53 65N35 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Compaan, E. Smoothing for the Zakharov and Klein-Gordon-Schrödinger systems on Euclidean spaces. (English) Zbl 1374.35342 SIAM J. Math. Anal. 49, No. 5, 4206-4231 (2017). MSC: 35Q53 35B41 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Antonelli, Paolo; Forcella, Luigi The electrostatic limit for the 3D Zakharov system. (English) Zbl 1375.35356 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 163, 19-33 (2017). MSC: 35Q35 76K05 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Fang, Yung-Fu; Shih, Hsi-Wei; Wang, Kuan-Hsiang Local well-posedness for the quantum Zakharov system in one spatial dimension. (English) Zbl 1364.35294 J. Hyperbolic Differ. Equ. 14, No. 1, 157-192 (2017). MSC: 35Q40 35L30 35L05 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI
Fang, Yung-Fu; Lin, Chi-Kun; Segata, Jun-Ichi The fourth-order nonlinear Schrödinger limit for quantum Zakharov system. (English) Zbl 1358.35169 Z. Angew. Math. Phys. 67, No. 6, Article ID 145, 27 p. (2016). MSC: 35Q55 35B30 35Q40 82D10 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Huang, Daiwen; Zhang, Jingjun Global smooth solutions for the nonlinear Schrödinger equation with magnetic effect. (English) Zbl 1356.35217 Discrete Contin. Dyn. Syst., Ser. S 9, No. 6, 1753-1773 (2016). MSC: 35Q55 35A01 35B40 35B65 35B45 × Cite Format Result Cite Review PDF Full Text: DOI
Shao, Shuanglin; Lin, Chi-Kun; Jiang, Jin-Cheng On one dimensional quantum Zakharov system. (English) Zbl 1353.35246 Discrete Contin. Dyn. Syst. 36, No. 10, 5445-5475 (2016). MSC: 35Q40 35L56 81Q99 35B65 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Cordero Ceballos, Juan Carlos Supersonic limit for the Zakharov-Rubenchik system. (English) Zbl 1347.35089 J. Differ. Equations 261, No. 9, 5260-5288 (2016). MSC: 35G31 35Q60 35Q55 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Gan, Zaihui; Ma, Yansheng; Zhong, Ting Some remarks on the blow-up rate for the 3D magnetic Zakharov system. (English) Zbl 1332.35049 J. Funct. Anal. 269, No. 8, 2505-2529 (2015). Reviewer: Dmitry Pelinovsky (Hamilton) MSC: 35B44 35B40 35Q60 82D10 76X05 × Cite Format Result Cite Review PDF Full Text: DOI
Barros, Vanessa; Linares, Felipe A remark on the well-posedness of a degenerated Zakharov system. (English) Zbl 1330.35086 Commun. Pure Appl. Anal. 14, No. 4, 1259-1274 (2015). MSC: 35G55 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Esfahani, Amin; Pastor, Ademir Well-posedness and orbital stability of traveling waves for the Schrödinger-improved Boussinesq system. (English) Zbl 1304.35186 Nonlinear Anal., Real World Appl. 22, 206-218 (2015). MSC: 35C07 35B35 35Q35 37K45 × Cite Format Result Cite Review PDF Full Text: DOI
Zhao, Xiaofei; Li, Ziyi Numerical methods and simulations for the dynamics of one-dimensional Zakharov-Rubenchik equations. (English) Zbl 1306.65248 J. Sci. Comput. 59, No. 2, 412-438 (2014). Reviewer: Qin Meng Zhao (Beijing) MSC: 65M06 65M70 35Q51 65M12 × Cite Format Result Cite Review PDF Full Text: DOI
Kishimoto, Nobu; Maeda, Masaya Construction of blow-up solutions for Zakharov system on \(\mathbb T^2\). (English) Zbl 1457.35069 Ann. Inst. Henri Poincaré, Anal. Non Linéaire 30, No. 5, 791-824 (2013). MSC: 35Q55 35B44 35A01 35L70 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gan, Zaihui; Guo, Boling; Huang, Daiwen Blow-up and nonlinear instability for the magnetic Zakharov system. (English) Zbl 1283.35109 J. Funct. Anal. 265, No. 6, 953-982 (2013). MSC: 35Q53 35Q60 35B44 82B10 78A02 76X05 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Jingjun; Guo, Chunxiao; Guo, Boling On the Cauchy problem for the magnetic Zakharov system. (English) Zbl 1442.76160 Monatsh. Math. 170, No. 1, 89-111 (2013). MSC: 76X05 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gan, Zai Hui; Guo, Bo Ling; Guo, Chun Xiao Blowing up of solutions to the Cauchy problem for the generalized Zakharov system with combined power-type nonlinearities. (English) Zbl 1260.35011 Acta Math. Sin., Engl. Ser. 28, No. 9, 1917-1936 (2012). MSC: 35B44 35A15 35Q55 35B30 × Cite Format Result Cite Review PDF Full Text: DOI
Han, Lijia; Zhang, Jingjun; Gan, Zaihui; Guo, Boling On the limit behavior of the magnetic Zakharov system. (English) Zbl 1238.35111 Sci. China, Math. 55, No. 3, 509-540 (2012). MSC: 35Q40 35L70 46E35 × Cite Format Result Cite Review PDF Full Text: DOI
Zhang, Jingjun; Guo, Yanfeng On the convergence of the solution for a generalized Zakharov system. (English) Zbl 1316.76117 J. Math. Phys. 52, No. 4, 043512, 12 p. (2011). MSC: 76X05 35Q35 35Q55 78A25 × Cite Format Result Cite Review PDF Full Text: DOI
Dias, João-Paulo; Figueira, Mário; Oliveira, Filipe On the Cauchy problem describing an electron-phonon interaction. (English) Zbl 1347.37128 Chin. Ann. Math., Ser. B 32, No. 4, 483-496 (2011). MSC: 37L50 35Q55 35B44 81V80 × Cite Format Result Cite Review PDF Full Text: DOI
Gan, Zaihui; Guo, Boling; Han, Lijia; Zhang, Jian Virial type blow-up solutions for the Zakharov system with magnetic field in a cold plasma. (English) Zbl 1248.35025 J. Funct. Anal. 261, No. 9, 2508-2528 (2011). Reviewer: Sebastien Boyabal (Chaville) MSC: 35B44 35Q55 35L70 76X05 82D10 × Cite Format Result Cite Review PDF Full Text: DOI
Bejenaru, Ioan; Herr, Sebastian Convolutions of singular measures and applications to the Zakharov system. (English) Zbl 1228.42027 J. Funct. Anal. 261, No. 2, 478-506 (2011). Reviewer: Dian K. Palagachev (Bari) MSC: 42B37 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Gan, Zaihui; Guo, Boling; Han, Lijia Optimal lower bound estimates for the blow-up rate for the Zakharov system in a nonhomogeneous medium. (English) Zbl 1217.35036 J. Math. Anal. Appl. 380, No. 1, 204-223 (2011). MSC: 35B44 35B45 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI
Gan, Zaihui; Guo, Boling Finite-time blowup for Zakharov system with combined power-type nonlinearities. (English) Zbl 1192.35027 Appl. Anal. 89, No. 5, 645-661 (2010). MSC: 35B44 35A15 35Q55 35B30 × Cite Format Result Cite Review PDF Full Text: DOI
Métivier, Guy Space propagation of instabilities in Zakharov equations. (English) Zbl 1143.78355 Physica D 237, No. 10-12, 1640-1654 (2008). MSC: 78A60 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI arXiv HAL
Texier, Benjamin Derivation of the Zakharov equations. (English) Zbl 1370.35249 Arch. Ration. Mech. Anal. 184, No. 1, 121-183 (2007). MSC: 35Q60 35L60 35B25 35S05 76F99 76X05 × Cite Format Result Cite Review PDF Full Text: DOI arXiv
Belaouar, R.; Colin, T.; Gallice, G.; Galusinski, C. Theoretical and numerical study of a quasi-linear Zakharov system describing Landau damping. (English) Zbl 1112.76090 ESAIM, Math. Model. Numer. Anal. 40, No. 6, 961-990 (2006). MSC: 76X05 76M20 35Q35 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI Numdam EuDML
Colin, M.; Colin, T. Cauchy problem and numerical simulation for a quasilinear Zakharov system describing laser-plasma interactions. (English) Zbl 1224.76186 Nonlinear Anal., Theory Methods Appl., Ser. A, Theory Methods 63, No. 5-7, e1679-e1686 (2005). MSC: 76X05 35Q55 82D10 × Cite Format Result Cite Review PDF Full Text: DOI
Colin, T.; Ebrard, G.; Gallice, G.; Texier, B. Justification of the Zakharov model from Klein-Gordon-wave systems. (English) Zbl 1063.35111 Commun. Partial Differ. Equations 29, No. 9-10, 1365-1401 (2004). MSC: 35L60 35Q55 78M35 × Cite Format Result Cite Review PDF Full Text: DOI
Yajima, Kenji; Zhang, Guoping Local smoothing property and Strichartz inequality for Schrödinger equations with potentials superquadratic at infinity. (English) Zbl 1060.35121 J. Differ. Equations 202, No. 1, 81-110 (2004). Reviewer: Horst Lange (Köln) MSC: 35Q40 81Q05 81Q20 × Cite Format Result Cite Review PDF Full Text: DOI
Oliveira, Filipe Stability of the solitons for the one-dimensional Zakharov-Rubenchik equation. (English) Zbl 1006.35084 Physica D 175, No. 3-4, 220-240 (2003). MSC: 35Q53 35Q51 × Cite Format Result Cite Review PDF Full Text: DOI
Colin, Thierry; Lannes, David Long-wave short-wave resonance for nonlinear geometric optics. (English) Zbl 1034.35133 Duke Math. J. 107, No. 2, 351-419 (2001). Reviewer: Alan Jeffrey (Newcastle upon Tyne) MSC: 35Q60 78A60 35B34 35B40 35C20 35L60 × Cite Format Result Cite Review PDF Full Text: DOI
Bidégaray, Brigitte The Cauchy problem for Schrödinger-Debye equations. (English) Zbl 1010.78010 Math. Models Methods Appl. Sci. 10, No. 3, 307-315 (2000). MSC: 78A60 35Q60 × Cite Format Result Cite Review PDF Full Text: DOI
Li, Yongsheng; Guo, Boling Attractor for dissipative Zakharov equations in an unbounded domain. (English) Zbl 0895.35096 Rev. Math. Phys. 9, No. 6, 675-687 (1997). MSC: 35Q55 76X05 × Cite Format Result Cite Review PDF Full Text: DOI
Ginibre, J.; Tsutsumi, Y.; Velo, G. On the Cauchy problem for the Zakharov system. (English) Zbl 0894.35108 J. Funct. Anal. 151, No. 2, 384-436 (1997). Reviewer: L.Vazquez (Madrid) MSC: 35Q55 82D10 76W05 × Cite Format Result Cite Review PDF Full Text: DOI
Colin, Thierry; Weinstein, Michael I. On the ground states of vector nonlinear Schrödinger equations. (English) Zbl 0863.35101 Ann. Inst. Henri Poincaré, Phys. Théor. 65, No. 1, 57-79 (1996). Reviewer: J.Ginibre (Orsay) MSC: 35Q55 76X05 35J50 35J60 35A15 × Cite Format Result Cite Review PDF Full Text: Numdam EuDML
Bergé, Luc; Bidégaray, Brigitte; Colin, Thierry A perturbative analysis of the time-envelope approximation in strong Langmuir turbulence. (English) Zbl 0899.76386 Physica D 95, No. 2-4, 351-379 (1996). MSC: 76X05 35L05 × Cite Format Result Cite Review PDF Full Text: DOI HAL
Merle, Frank Blow-up results of virial type for Zakharov equations. (English) Zbl 0858.35117 Commun. Math. Phys. 175, No. 2, 433-455 (1996). Reviewer: B.A.Malomed (Tel Aviv) MSC: 35Q55 35B40 × Cite Format Result Cite Review PDF Full Text: DOI
Glangetas, L.; Merle, F. Concentration properties of blow-up solutions and instability results for Zakharov equation in dimension two. II. (English) Zbl 0808.35138 Commun. Math. Phys. 160, No. 2, 349-389 (1994). MSC: 35Q55 35B40 76X05 × Cite Format Result Cite Review PDF Full Text: DOI
Glangetas, L.; Merle, F. Existence of self-similar blow-up solutions for Zakharov equation in dimension two. I. (English) Zbl 0808.35137 Commun. Math. Phys. 160, No. 1, 173-215 (1994). MSC: 35Q55 35B40 76X05 × Cite Format Result Cite Review PDF Full Text: DOI
Ozawa, Tohru; Tsutsumi, Yoshio The nonlinear Schrödinger limit and the initial layer of the Zakharov equations. (English) Zbl 0754.35113 Proc. Japan Acad., Ser. A 67, No. 4, 113-116 (1991). Reviewer: Guo Boling (Beijing) MSC: 35Q35 76X05 82D10 35Q55 × Cite Format Result Cite Review PDF Full Text: DOI