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Justification of and long-wave correction to Davey-Stewartson systems from quadratic hyperbolic systems
1. | MAB, Université Bordeaux I and CNRS UMR 5466, 351 Cours de la Libération, 33405 Talence Cedex, France, France |
[1] |
Caroline Obrecht, J.-C. Saut. Remarks on the full dispersion Davey-Stewartson systems. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1547-1561. doi: 10.3934/cpaa.2015.14.1547 |
[2] |
Uchida Hidetake. Analytic smoothing effect and global existence of small solutions for the elliptic-hyperbolic Davey-Stewartson system. Conference Publications, 2001, 2001 (Special) : 182-190. doi: 10.3934/proc.2001.2001.182 |
[3] |
Christian Klein, Jean-Claude Saut. A numerical approach to Blow-up issues for Davey-Stewartson II systems. Communications on Pure and Applied Analysis, 2015, 14 (4) : 1443-1467. doi: 10.3934/cpaa.2015.14.1443 |
[4] |
Christian Klein, Benson Muite, Kristelle Roidot. Numerical study of blow-up in the Davey-Stewartson system. Discrete and Continuous Dynamical Systems - B, 2013, 18 (5) : 1361-1387. doi: 10.3934/dcdsb.2013.18.1361 |
[5] |
Jing Lu, Yifei Wu. Sharp threshold for scattering of a generalized Davey-Stewartson system in three dimension. Communications on Pure and Applied Analysis, 2015, 14 (5) : 1641-1670. doi: 10.3934/cpaa.2015.14.1641 |
[6] |
Olivier Goubet, Manal Hussein. Global attractor for the Davey-Stewartson system on $\mathbb R^2$. Communications on Pure and Applied Analysis, 2009, 8 (5) : 1555-1575. doi: 10.3934/cpaa.2009.8.1555 |
[7] |
Shiming Li, Yongsheng Li, Wei Yan. A global existence and blow-up threshold for Davey-Stewartson equations in $\mathbb{R}^3$. Discrete and Continuous Dynamical Systems - S, 2016, 9 (6) : 1899-1912. doi: 10.3934/dcdss.2016077 |
[8] |
Zaihui Gan, Boling Guo, Jian Zhang. Sharp threshold of global existence for the generalized Davey-Stewartson system in $R^2$. Communications on Pure and Applied Analysis, 2009, 8 (3) : 913-922. doi: 10.3934/cpaa.2009.8.913 |
[9] |
Yahong Peng, Yaguang Wang. Reflection of highly oscillatory waves with continuous oscillatory spectra for semilinear hyperbolic systems. Discrete and Continuous Dynamical Systems, 2009, 24 (4) : 1293-1306. doi: 10.3934/dcds.2009.24.1293 |
[10] |
Yue-Jun Peng, Yong-Fu Yang. Long-time behavior and stability of entropy solutions for linearly degenerate hyperbolic systems of rich type. Discrete and Continuous Dynamical Systems, 2015, 35 (8) : 3683-3706. doi: 10.3934/dcds.2015.35.3683 |
[11] |
Gilles Carbou, Pierre Fabrie, Olivier Guès. On the Ferromagnetism equations in the non static case. Communications on Pure and Applied Analysis, 2004, 3 (3) : 367-393. doi: 10.3934/cpaa.2004.3.367 |
[12] |
Jerry L. Bona, Thierry Colin, Colette Guillopé. Propagation of long-crested water waves. Discrete and Continuous Dynamical Systems, 2013, 33 (2) : 599-628. doi: 10.3934/dcds.2013.33.599 |
[13] |
Michiel Bertsch, Hirofumi Izuhara, Masayasu Mimura, Tohru Wakasa. Standing and travelling waves in a parabolic-hyperbolic system. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5603-5635. doi: 10.3934/dcds.2019246 |
[14] |
Jerry L. Bona, Thierry Colin, Colette Guillopé. Propagation of long-crested water waves. Ⅱ. Bore propagation. Discrete and Continuous Dynamical Systems, 2019, 39 (10) : 5543-5569. doi: 10.3934/dcds.2019244 |
[15] |
Youcef Mammeri. On the decay in time of solutions of some generalized regularized long waves equations. Communications on Pure and Applied Analysis, 2008, 7 (3) : 513-532. doi: 10.3934/cpaa.2008.7.513 |
[16] |
Amjad Khan, Dmitry E. Pelinovsky. Long-time stability of small FPU solitary waves. Discrete and Continuous Dynamical Systems, 2017, 37 (4) : 2065-2075. doi: 10.3934/dcds.2017088 |
[17] |
Fabio Ancona, Andrea Marson. On the Glimm Functional for general hyperbolic systems. Conference Publications, 2011, 2011 (Special) : 44-53. doi: 10.3934/proc.2011.2011.44 |
[18] |
Matthew Nicol. Induced maps of hyperbolic Bernoulli systems. Discrete and Continuous Dynamical Systems, 2001, 7 (1) : 147-154. doi: 10.3934/dcds.2001.7.147 |
[19] |
Tai-Ping Liu, Shih-Hsien Yu. Hyperbolic conservation laws and dynamic systems. Discrete and Continuous Dynamical Systems, 2000, 6 (1) : 143-145. doi: 10.3934/dcds.2000.6.143 |
[20] |
Jerry Bona, Hongqiu Chen. Solitary waves in nonlinear dispersive systems. Discrete and Continuous Dynamical Systems - B, 2002, 2 (3) : 313-378. doi: 10.3934/dcdsb.2002.2.313 |
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