Yu, Xueying; Yue, Haitian; Zhao, Zehua Global well-posedness and scattering for fourth-order Schrödinger equations on waveguide manifolds. (English) Zbl 07809895 SIAM J. Math. Anal. 56, No. 1, 1427-1458 (2024). MSC: 35Q55 35Q41 35C08 35R01 37K06 37L50 35P25 35B40 35A01 35A02 PDFBibTeX XMLCite \textit{X. Yu} et al., SIAM J. Math. Anal. 56, No. 1, 1427--1458 (2024; Zbl 07809895) Full Text: DOI arXiv
Singh, Shailendra; Saha Ray, S. Bilinear representation, bilinear Bäcklund transformation, Lax pair and analytical solutions for the fourth-order potential Ito equation describing water waves via Bell polynomials. (English) Zbl 1526.35105 J. Math. Anal. Appl. 530, No. 2, Article ID 127695, 15 p. (2024). MSC: 35C05 35A22 37K10 PDFBibTeX XMLCite \textit{S. Singh} and \textit{S. Saha Ray}, J. Math. Anal. Appl. 530, No. 2, Article ID 127695, 15 p. (2024; Zbl 1526.35105) Full Text: DOI
Yu, Xueying; Yue, Haitian; Zhao, Zehua On the decay property of the cubic fourth-order Schrödinger equation. (English) Zbl 1512.35559 Proc. Am. Math. Soc. 151, No. 6, 2619-2630 (2023). MSC: 35Q55 35Q41 35R01 37K06 37L50 35B65 PDFBibTeX XMLCite \textit{X. Yu} et al., Proc. Am. Math. Soc. 151, No. 6, 2619--2630 (2023; Zbl 1512.35559) Full Text: DOI arXiv
Czaja, Radosław; Kania, Maria Exponential attractors for modified Swift-Hohenberg equation in \(\mathbb{R}^N\). (English) Zbl 1524.37073 Differ. Integral Equ. 36, No. 5-6, 347-366 (2023). Reviewer: Philippe Laurençot (Chambéry) MSC: 37L30 35B41 35G25 35Q92 PDFBibTeX XMLCite \textit{R. Czaja} and \textit{M. Kania}, Differ. Integral Equ. 36, No. 5--6, 347--366 (2023; Zbl 1524.37073) Full Text: DOI
Zhou, Huaxin; Yu, Jing; Han, Jingwei Several exact solutions of the reduced fourth-order flow equation of the Kaup-Newell system. (English) Zbl 1524.35571 Wave Motion 109, Article ID 102840, 12 p. (2022). MSC: 35Q53 35Q55 35C08 37K40 PDFBibTeX XMLCite \textit{H. Zhou} et al., Wave Motion 109, Article ID 102840, 12 p. (2022; Zbl 1524.35571) Full Text: DOI
Baleanu, Dumitru; Alshomrani, Ali Saleh; Ullah, Malik Zaka A new fourth-order integrable nonlinear equation: breather, rogue waves, other lump interaction phenomena, and conservation laws. (English) Zbl 1494.35138 Adv. Difference Equ. 2021, Paper No. 195, 16 p. (2021). MSC: 35Q51 37K40 35C08 PDFBibTeX XMLCite \textit{D. Baleanu} et al., Adv. Difference Equ. 2021, Paper No. 195, 16 p. (2021; Zbl 1494.35138) Full Text: DOI
Hu, Beibei; Zhang, Ling; Li, Qinghong; Zhang, Ning Riemann-Hilbert problem associated with the fourth-order dispersive nonlinear Schrödinger equation in optics and magnetic mechanics. (English) Zbl 1482.35077 J. Nonlinear Math. Phys. 28, No. 4, 414-435 (2021). MSC: 35G31 35Q15 35Q60 37N15 PDFBibTeX XMLCite \textit{B. Hu} et al., J. Nonlinear Math. Phys. 28, No. 4, 414--435 (2021; Zbl 1482.35077) Full Text: DOI arXiv
Meng, Gao-Qing; Pan, Yu-Song; Xie, Xi-Yang Deformed breather and rogue waves for the inhomogeneous fourth-order nonlinear Schrödinger equation in alpha-helical proteins. (English) Zbl 1516.37120 Nonlinear Dyn. 100, No. 3, 2779-2795 (2020). MSC: 37K40 35C08 35Q55 37K35 PDFBibTeX XMLCite \textit{G.-Q. Meng} et al., Nonlinear Dyn. 100, No. 3, 2779--2795 (2020; Zbl 1516.37120) Full Text: DOI
Lan, Zhong-Zhou Rogue wave solutions for a coupled nonlinear Schrödinger equation in the birefringent optical fiber. (English) Zbl 1428.35522 Appl. Math. Lett. 98, 128-134 (2019). MSC: 35Q55 78A60 37K35 68W30 PDFBibTeX XMLCite \textit{Z.-Z. Lan}, Appl. Math. Lett. 98, 128--134 (2019; Zbl 1428.35522) Full Text: DOI
Dai, Huiju; Li, Lianzhong; Wang, Qi; Sha, An Lie symmetry analysis, Bäcklund transformation and exact solutions for a class of fourth-order partial differential equations. (Chinese. English summary) Zbl 1438.35006 J. East China Norm. Univ., Nat. Sci. Ed. 2019, No. 1, 24-31 (2019). MSC: 35A30 35G20 37K35 PDFBibTeX XMLCite \textit{H. Dai} et al., J. East China Norm. Univ., Nat. Sci. Ed. 2019, No. 1, 24--31 (2019; Zbl 1438.35006)
Oh, Tadahiro; Wang, Yuzhao Global well-posedness of the periodic cubic fourth order NLS in negative Sobolev spaces. (English) Zbl 1431.35178 Forum Math. Sigma 6, Paper No. e5, 80 p. (2018). Reviewer: Vincent Lescarret (Gif-sur-Yvette) MSC: 35Q55 35A01 35A02 37G05 35R25 PDFBibTeX XMLCite \textit{T. Oh} and \textit{Y. Wang}, Forum Math. Sigma 6, Paper No. e5, 80 p. (2018; Zbl 1431.35178) Full Text: DOI arXiv
Yang, Jin-Wei; Gao, Yi-Tian; Su, Chuan-Qi; Wang, Qi-Min; Lan, Zhong-Zhou Breathers and rogue waves in a Heisenberg ferromagnetic spin chain or an alpha helical protein. (English) Zbl 1510.35316 Commun. Nonlinear Sci. Numer. Simul. 48, 340-349 (2017). MSC: 35Q55 35A30 37K40 82C10 PDFBibTeX XMLCite \textit{J.-W. Yang} et al., Commun. Nonlinear Sci. Numer. Simul. 48, 340--349 (2017; Zbl 1510.35316) Full Text: DOI
Lu, Shiping; Zhong, Tao Two homoclinic solutions for a nonperiodic fourth-order differential equation without coercive condition. (English) Zbl 1369.34066 Math. Methods Appl. Sci. 40, No. 8, 3163-3172 (2017). MSC: 34C37 34A34 58E50 37C60 PDFBibTeX XMLCite \textit{S. Lu} and \textit{T. Zhong}, Math. Methods Appl. Sci. 40, No. 8, 3163--3172 (2017; Zbl 1369.34066) Full Text: DOI
Saanouni, Tarek Decay of solutions to a fourth-order nonlinear Schrödinger equation. (English) Zbl 1359.35180 Analysis, München 37, No. 1, 47-54 (2017). MSC: 35Q55 35B40 35B33 37K05 37L50 35P25 35L76 PDFBibTeX XMLCite \textit{T. Saanouni}, Analysis, München 37, No. 1, 47--54 (2017; Zbl 1359.35180) Full Text: DOI
Yang, Chunyan; Li, Xiaoqing The symmetry and series solutions of a class of fourth-order partial differential equation. (Chinese. English summary) Zbl 1374.35027 Pure Appl. Math. 32, No. 4, 432-440 (2016). MSC: 35B06 37J15 35G20 PDFBibTeX XMLCite \textit{C. Yang} and \textit{X. Li}, Pure Appl. Math. 32, No. 4, 432--440 (2016; Zbl 1374.35027) Full Text: DOI
Natali, Fábio; Pastor, Ademir The fourth-order dispersive nonlinear Schrödinger equation: orbital stability of a standing wave. (English) Zbl 1331.35325 SIAM J. Appl. Dyn. Syst. 14, No. 3, 1326-1347 (2015). Reviewer: Alain Brillard (Riedisheim) MSC: 35Q55 35B35 37K45 76B25 PDFBibTeX XMLCite \textit{F. Natali} and \textit{A. Pastor}, SIAM J. Appl. Dyn. Syst. 14, No. 3, 1326--1347 (2015; Zbl 1331.35325) Full Text: DOI arXiv
Vakhnenko, Oleksiy O. Semidiscrete integrable nonlinear systems generated by the new fourth-order spectral operator: local conservation laws. (English) Zbl 1256.35141 J. Nonlinear Math. Phys. 18, No. 3, 401-414 (2011). MSC: 35Q55 35P30 37K60 PDFBibTeX XMLCite \textit{O. O. Vakhnenko}, J. Nonlinear Math. Phys. 18, No. 3, 401--414 (2011; Zbl 1256.35141) Full Text: DOI
Rätz, Andreas; Voigt, A. A diffuse-interface approximation for surface diffusion including adatoms. (English) Zbl 1117.35315 Nonlinearity 20, No. 1, 177-192 (2007). MSC: 35K55 35K65 37E35 53C44 35K25 PDFBibTeX XMLCite \textit{A. Rätz} and \textit{A. Voigt}, Nonlinearity 20, No. 1, 177--192 (2007; Zbl 1117.35315) Full Text: DOI
Magnitskii, N. A.; Sidorov, S. V. On the transition to diffusion chaos through a subharmonic cascade of bifurcations of two-dimensional tori: numerical analysis. (English. Russian original) Zbl 1124.37047 Differ. Equ. 41, No. 11, 1626-1634 (2005); translation from Differ. Uravn. 41, No. 11, 1550-1559 (2005). MSC: 37L10 37D45 65P20 35K57 35Q55 PDFBibTeX XMLCite \textit{N. A. Magnitskii} and \textit{S. V. Sidorov}, Differ. Equ. 41, No. 11, 1626--1634 (2005; Zbl 1124.37047); translation from Differ. Uravn. 41, No. 11, 1550--1559 (2005) Full Text: DOI
Zhang, Suying; Deng, Zichen A simple and efficient fourth-order approximation solution for nonlinear dynamic system. (English) Zbl 1046.37055 Mech. Res. Commun. 31, No. 2, 221-228 (2004). MSC: 37M15 65F30 65L05 34C60 34C29 PDFBibTeX XMLCite \textit{S. Zhang} and \textit{Z. Deng}, Mech. Res. Commun. 31, No. 2, 221--228 (2004; Zbl 1046.37055) Full Text: DOI
van den Berg, Jan Bouwe; Hulshof, Josephus; VanderVorst, Robertus C. Travelling waves for fourth order parabolic equations. (English) Zbl 0988.34035 SIAM J. Math. Anal. 32, No. 6, 1342-1374 (2001). MSC: 34C60 34A34 34C37 34C23 35A18 35K25 35K55 37B25 37C29 34C20 PDFBibTeX XMLCite \textit{J. B. van den Berg} et al., SIAM J. Math. Anal. 32, No. 6, 1342--1374 (2001; Zbl 0988.34035) Full Text: DOI
Owren, B.; Marthinsen, A. Runge-Kutta methods adapted to manifolds and based on rigid frames. (English) Zbl 0919.65049 BIT 39, No. 1, 116-142 (1999). Reviewer: M.Calvo (Zaragoza) MSC: 65L06 34A34 37-XX 65L05 70E15 PDFBibTeX XMLCite \textit{B. Owren} and \textit{A. Marthinsen}, BIT 39, No. 1, 116--142 (1999; Zbl 0919.65049) Full Text: DOI
Brown, Ray; Chua, Leon O. Dynamical integration. (English) Zbl 0872.65062 Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 217-222 (1993). MSC: 65L05 34A34 37D45 PDFBibTeX XMLCite \textit{R. Brown} and \textit{L. O. Chua}, Int. J. Bifurcation Chaos Appl. Sci. Eng. 3, No. 1, 217--222 (1993; Zbl 0872.65062) Full Text: DOI
Kalantarov, V. K. Global behavior of the solutions of certain fourth-order nonlinear equations. (English. Russian original) Zbl 0696.35147 J. Sov. Math. 49, No. 5, 1160-1166 (1990); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 163, 66-75 (1987). MSC: 35Q99 37C70 35G20 35B65 PDFBibTeX XMLCite \textit{V. K. Kalantarov}, J. Sov. Math. 49, No. 5, 1160--1166 (1990; Zbl 0696.35147); translation from Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 163, 66--75 (1987) Full Text: DOI
Makhmudov, A. P.; Aliev, Z. S. Some global results for linearizable and nonlinearizable Sturm-Liouville problems of fourth order. (English. Russian original) Zbl 0779.34025 Sov. Math., Dokl. 40, No. 3, 472-476 (1990); translation from Dokl. Akad. Nauk SSSR 309, No. 1, 34-38 (1989). MSC: 34B24 37G99 PDFBibTeX XMLCite \textit{A. P. Makhmudov} and \textit{Z. S. Aliev}, Sov. Math., Dokl. 40, No. 3, 472--476 (1989; Zbl 0779.34025); translation from Dokl. Akad. Nauk SSSR 309, No. 1, 34--38 (1989)
Kalantarov, V. K. On the global behaviour of solutions of some fourth order nonlinear equations. (Russian. English summary) Zbl 0668.35080 Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 163, 66-75 (1987). MSC: 35Q99 37C70 35G20 35B65 PDFBibTeX XMLCite \textit{V. K. Kalantarov}, Zap. Nauchn. Semin. Leningr. Otd. Mat. Inst. Steklova 163, 66--75 (1987; Zbl 0668.35080) Full Text: EuDML
Collet, P.; Eckmann, J. P The existence of dendritic fronts. (English) Zbl 0711.35061 Commun. Math. Phys. 107, No. 1, 39-92 (1986). MSC: 35K55 58J47 37N99 PDFBibTeX XMLCite \textit{P. Collet} and \textit{J. P Eckmann}, Commun. Math. Phys. 107, 39--92 (1986; Zbl 0711.35061) Full Text: DOI
Ekeland, I. Dual variational methods in non-convex optimization and differential equations. (English) Zbl 0544.49010 Mathematical theories of optimization, Proc. Conf., Genova 1981, Lect. Notes Math. 979, 108-120 (1983). Reviewer: C.L.Sandblom MSC: 49N15 49J45 90C48 49J27 49K15 49K20 49K27 58C20 58E30 37J99 35L70 PDFBibTeX XML