Preface: Nonlinear waves in fluids in honor of Roger Grimshaw on the occasion of his 80th birthday. (English) Zbl 1418.00025
From the text: This special issue Studies in Applied Mathematics and the one that follows [Zbl 1418.00026] are dedicated to Prof. Roger H. J. Grimshaw on the occasion of his 80th birthday.
MSC:
| 00B15 | Collections of articles of miscellaneous specific interest |
| 76-06 | Proceedings, conferences, collections, etc. pertaining to fluid mechanics |
| 01A70 | Biographies, obituaries, personalia, bibliographies |
Biographic References:
Grimshaw, RogerCitations:
Zbl 1418.00026References:
| [1] | GrimshawR.The solitary wave in water of variable depth. J Fluid Mech.1970;42:639-656. · Zbl 0193.27304 |
| [2] | GrimshawR.The solitary wave in water of variable depth. Part 2. J Fluid Mech.1971;46:611-622. · Zbl 0222.76017 |
| [3] | GrimshawR.Slowly varying solitary waves. I Korteweg‐de Vries equation. Proc Roy Soc.1979;368A:359-375. · Zbl 0414.76017 |
| [4] | GrimshawR, StewartsonK.Slowly varying solitary waves. II Nonlinear Schrödinger equation. Proc Roy Soc.1979;368A:377-388. · Zbl 0416.76014 |
| [5] | GrimshawRHJ. The modulation of an internal gravity‐wave packet, and the resonance with the mean motion. Stud Appl Math.1977;56:241-266. · Zbl 0361.76029 |
| [6] | GrimshawR.Mean flows induced by internal gravity wave packets propagating in a shear flow. Phil Trans Roy Soc.1979;292A:391-417. · Zbl 0497.76021 |
| [7] | GrimshawR.Evolution equations for long nonlinear internal waves in stratified shear flows. Stud Appl Math.1981;65:159-188. · Zbl 0492.76035 |
| [8] | GrimshawR.Wave action and wave‐mean flow interaction, with application to stratified shear flows. Ann Rev Fluid Mech.1984;16:11-44. · Zbl 0599.76024 |
| [9] | GrimshawR.Evolution equations for weakly nonlinear, long internal waves in a rotating fluid. Stud Appl Math.1985;73:1-33. · Zbl 0572.76102 |
| [10] | GearJ, GrimshawR.Weak and strong interactions between internal solitary waves. Stud Appl Math.1984;70:235-258. · Zbl 0548.76020 |
| [11] | GrimshawR.Resonant wave interactions near a critical level in a stratified shear flow. J Fluid Mech.1994;269:1-22. · Zbl 0809.76007 |
| [12] | Grimshaw RHJ, SmythNF.Resonant flow of a stratified fluid over topography. J Fluid Mech.1986;169:429-464. · Zbl 0614.76108 |
| [13] | Grimshaw, RHJ, Zhang D‐H, ChowKW.Transcritical flow over a hole. Stud Appl Math.2009;122:235-248. · Zbl 1177.37068 |
| [14] | GrimshawR, PelinovskyD, PelinovskyE, TalipovaT.Wave group dynamics in weakly nonlinear long‐wave models. Physica D2001;159:35-57. · Zbl 1006.76012 |
| [15] | ElGA, GrimshawRHJ, KamchatnovAM.Wave breaking and the generation of undular bores in an integrable shallow‐water system. Stud Appl Math.2005;114:395-411. · Zbl 1145.76327 |
| [16] | ElGA, GrimshawRHJ, SmythNF.Unsteady undular bores in fully nonlinear shallow‐water theory. Phys Fluids2006;18:027104 (17 pages). · Zbl 1185.76454 |
| [17] | GrimshawR, PelinovskyE, TalipovaT, KurkinaA.Internal solitary waves: Propagation, deformation and disintegration. Nonlin Process Geophys.2010;17:633-649. |
| [18] | Grimshaw RHJ, OstrovskyLA, ShriraVI, StepanyantsYA. Long nonlinear surface and internal gravity waves in a rotating ocean. Surv. Geophys.1998;19:289-338. |
| [19] | GrimshawR, HelfrichKR.Long‐time solutions of the Ostrovsky equation. Stud Appl Math.2008;121:71-88. · Zbl 1194.35366 |
| [20] | GrimshawR, HelfrichK, JohnsonE.The reduced Ostrovsky equation: Integrability and breaking. Stud Appl Math.2012;129:414-436. · Zbl 1291.35019 |
| [21] | GrimshawR, HelfrichK, JohnsonE.Experimental study of the effect of rotation on large amplitude internal waves. Phys. Fluids2013;25:056602. |
| [22] | AkylasTR, GrimshawRHJ. Solitary internal waves with oscillatory tails. J Fluid Mech.1992;242:279-298. · Zbl 0754.76014 |
| [23] | GrimshawR, JoshiN.Weakly non‐local solitary waves in a singularly perturbed Korteweg‐de Vries equation. SIAM J Appl Math.1995;55:124-135. · Zbl 0814.34043 |
| [24] | GottwaldG, GrimshawR.The formation of coherent structures in the context of blocking. J Atmos Sci.1999;56:3640-3662. |
| [25] | NitscheM, WeidmanPD, GrimshawR, GhristM, FornbergB.Evolution of solitary waves in a two‐pycnocline system. J Fluid Mech.2010;642:235-277. · Zbl 1183.76650 |
| [26] | AliasA, GrimshawRHJ, KhusnutdinovaKR.Coupled Ostrovsky equations for internal waves in a shear flowPhys. Fluids2014;26:126603. |
| [27] | GrimshawR.Nonlinear wave equations for oceanic internal solitary waves. Stud Appl Math.2016;136:214-237. · Zbl 1332.35287 |
| [28] | GrimshawR, YuanC.The propagation of internal undular bores over variable topography. Physica D2016;333:200-207. · Zbl 1415.35240 |
| [29] | GrimshawR, HelfrichKR.Internal solitary wave generation by tidal flow over topography. J Fluid Mech.2018;839:387-407. · Zbl 1419.76113 |
| [30] | HoeferMA, SmythNF, SprengerP.Modulation theory solution for nonlinearly resonant, fifth‐order Korteweg‐de Vries, nonclassical, traveling dispersive shock waves. Stud Appl Math. 2019;142:219-240. · Zbl 1418.35305 |
| [31] | CongyT, ElGA, HoeferMA, ShearerM.Nonlinear Schrödinger equations and the universal description of dispersive shock wave structure. Stud Appl Math. 2019;142:241-268. · Zbl 1418.35334 |
| [32] | AblowitzMJ, ColeJT, RumanovI.On the Whitham system for the radial nonlinear Schrödinger equation. Stud Appl Math. 2019;142:269-313. · Zbl 1418.35332 |
| [33] | BridgesTJ, RatliffDJ.Krein signature and Whitham modulation theory: The sign of characteristics and the “sign characteristic”. Stud Appl Math. 2019;142:314-335. · Zbl 1418.35321 |
| [34] | DhaouadiF, FavrieN, GavrilyukS.Extended Lagrangian approach for the defocusing nonlinear Schrödinger equation. Stud Appl Math. 2019;142:336-358. · Zbl 1418.35335 |
| [35] | JoshiN, LustriCJ.Generalized solitary waves in a finite‐difference Korteweg‐de Vries Equation. Stud Appl Math. 2019;142:359-384. · Zbl 1418.35324 |
| [36] | SlunyaevA.On the optimal focusing of solitons and breathers in long wave models. Stud Appl Math. 2019;142:385-413. · Zbl 1418.35331 |
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