TRAVELING WATER WAVES - THE EBB AND FLOW OF TWO CENTURIES

被引：32

作者：

Haziot, Susanna V. ^{[1
]}

Hur, Vera Mikyoung ^{[2
]}

Strauss, Walter A. ^{[3
,4
]}

Toland, J. F. ^{[5
]}

Wahlen, Erik ^{[6
]}

Walsh, Samuel ^{[7
]}

Wheeler, Miles H. ^{[5
]}

机构：

[1] Univ Wien, Fak Math, Oskar Morgenstern Pl 1, A-1090 Vienna, Austria

[2] Univ Illinois, Dept Math, Urbana, IL 61801 USA

[3] Brown Univ, Dept Math, Providence, RI 02912 USA

[4] Brown Univ, Lefschetz Ctr Dynam Syst, Providence, RI 02912 USA

[5] Univ Bath, Dept Math Sci, Bath BA2 7AY, Avon, England

[6] Lund Univ, Ctr Math Sci, POB 118, S-22100 Lund, Sweden

[7] Univ Missouri, Dept Math, 202 Math Sci Bldg, Columbia, MO 65211 USA

来源：

QUARTERLY OF APPLIED MATHEMATICS | 2022年 / 80卷 / 02期

基金：

瑞典研究理事会; 奥地利科学基金会; 欧洲研究理事会;

关键词：

GRAVITY-CAPILLARY WAVES; CONDITIONAL ENERGETIC STABILITY; GLOBAL BIFURCATION-THEORY; LOCALIZED SOLITARY-WAVE; SPIKE-LAYER SOLUTIONS; ALMOST-HIGHEST WAVE; SURFACE-TENSION-I; STOKES WAVES; AMPLITUDE SOLITARY; DEEP-WATER;

D O I：

10.1090/qam/1614

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This survey covers the mathematical theory of steady water waves with an emphasis on topics that are at the forefront of current research. These areas include: variational characterizations of traveling water waves; analytical and numerical studies of periodic waves with critical layers that may overhang; existence, nonexistence, and qualitative theory of solitary waves and fronts; traveling waves with localized vorticity or density stratification; and waves in three dimensions.

引用

页码：317 / 401

页数：85

共 271 条

[1] EVOLUTION OF PACKETS OF WATER-WAVES [J].

ABLOWITZ, MJ ;

SEGUR, H .

JOURNAL OF FLUID MECHANICS, 1979, 92 (JUN) :691-715

[2] Three-dimensional overturned traveling water waves [J].

Akers, Benjamin F. ;

Reeger, Jonah A. .

WAVE MOTION, 2017, 68 :210-217

[3] Global bifurcation theory for periodic traveling interfacial gravity-capillary waves [J].

Ambrose, David M. ;

Strauss, Walter A. ;

Wright, J. Douglas .

ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2016, 33 (04) :1081-1101

[4]

Amick C.J., 1984, Ann. Sc. Norm. Super. Pisa, Cl. Sci., V11, P441

[5] A GLOBAL THEORY OF INTERNAL SOLITARY WAVES IN 2-FLUID SYSTEMS [J].

AMICK, CJ ;

TURNER, REL .

TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY, 1986, 298 (02) :431-484

[6] BOUNDS FOR WATER-WAVES [J].

AMICK, CJ .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1987, 99 (02) :91-114

[7] ON PERIODIC WATER-WAVES AND THEIR CONVERGENCE TO SOLITARY WAVES IN THE LONG-WAVE LIMIT [J].

AMICK, CJ ;

TOLAND, JF .

PHILOSOPHICAL TRANSACTIONS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 1981, 303 (1481) :633-669

[8] ON THE STOKES CONJECTURE FOR THE WAVE OF EXTREME FORM [J].

AMICK, CJ ;

FRAENKEL, LE ;

TOLAND, JF .

ACTA MATHEMATICA, 1982, 148 :193-214

[9]

AMICK CJ, 1981, ARCH RATION MECH AN, V76, P9, DOI 10.1007/BF00250799

[10] SOLITARY WAVES WITH SURFACE TENSION-I - TRAJECTORIES HOMOCLINIC TO PERIODIC-ORBITS IN 4 DIMENSIONS [J].

AMICK, CJ ;

TOLAND, JF .

ARCHIVE FOR RATIONAL MECHANICS AND ANALYSIS, 1992, 118 (01) :37-69

← 1 2 3 4 5 6 7 8 9 10 →