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Benjamin–Ono equation

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A two-parameter Miura transformation of the Benjamin-Ono equation, T.L. Bock, M.D. Kruskal, Physics Letters A, Volume 74, Issues 3–4, 12 November 1979, Pages 173-176.
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It possesses infinitely many conserved densities and symmetries; thus it is a completely integrable system.
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Ono, Hiroaki (1975), "Algebraic solitary waves in stratified fluids",
169:(1967), "Internal waves of permanent form in fluids of great depth", 334: 277: 48: 102: 248:Benjamin-Ono equations: Solitons and Shock Waves 354: 297: 8: 361: 347: 304: 290: 85: 69: 53: 47: 380:Nonlinear partial differential equations 207:Journal of the Physical Society of Japan 29: 145: 103:{\displaystyle u_{t}+uu_{x}+Hu_{xx}=0} 7: 315: 313: 258: 256: 28:in deep water. It was introduced by 33: 14: 317: 260: 24:that describes one-dimensional 1: 39:The Benjamin–Ono equation is 22:integro-differential equation 333:. You can help Knowledge by 276:. You can help Knowledge by 411: 312: 255: 171:Journal of Fluid Mechanics 395:Theoretical physics stubs 390:Applied mathematics stubs 191:10.1017/s002211206700103x 20:is a nonlinear partial 272:-related article is a 104: 105: 18:Benjamin–Ono equation 227:10.1143/JPSJ.39.1082 46: 16:In mathematics, the 327:theoretical physics 325:This article about 270:applied mathematics 219:1975JPSJ...39.1082O 183:1967JFM....29..559B 167:Benjamin, T. Brooke 134:Bretherton equation 385:Integrable systems 100: 342: 341: 285: 284: 119:Hilbert transform 402: 363: 356: 349: 321: 314: 306: 299: 292: 264: 257: 237: 213:(4): 1082–1091, 201: 153: 150: 109: 107: 106: 101: 93: 92: 74: 73: 58: 57: 410: 409: 405: 404: 403: 401: 400: 399: 370: 369: 368: 367: 311: 310: 253: 244: 204: 165: 162: 157: 156: 151: 147: 142: 130: 81: 65: 49: 44: 43: 30:Benjamin (1967) 12: 11: 5: 408: 406: 398: 397: 392: 387: 382: 372: 371: 366: 365: 358: 351: 343: 340: 339: 322: 309: 308: 301: 294: 286: 283: 282: 265: 251: 250: 243: 242:External links 240: 239: 238: 202: 161: 158: 155: 154: 144: 143: 141: 138: 137: 136: 129: 126: 111: 110: 99: 96: 91: 88: 84: 80: 77: 72: 68: 64: 61: 56: 52: 26:internal waves 13: 10: 9: 6: 4: 3: 2: 407: 396: 393: 391: 388: 386: 383: 381: 378: 377: 375: 364: 359: 357: 352: 350: 345: 344: 338: 336: 332: 328: 323: 320: 316: 307: 302: 300: 295: 293: 288: 287: 281: 279: 275: 271: 266: 263: 259: 254: 249: 246: 245: 241: 236: 232: 228: 224: 220: 216: 212: 208: 203: 200: 196: 192: 188: 184: 180: 176: 172: 168: 164: 163: 159: 149: 146: 139: 135: 132: 131: 127: 125: 122: 120: 116: 97: 94: 89: 86: 82: 78: 75: 70: 66: 62: 59: 54: 50: 42: 41: 40: 37: 35: 31: 27: 23: 19: 335:expanding it 324: 278:expanding it 267: 252: 210: 206: 174: 170: 148: 123: 114: 112: 38: 17: 15: 374:Categories 177:(3): 559, 140:References 34:Ono (1975) 199:123065419 128:See also 235:0398275 215:Bibcode 179:Bibcode 160:Sources 117:is the 233:  197:  113:where 329:is a 268:This 195:S2CID 331:stub 274:stub 32:and 223:doi 187:doi 376:: 231:MR 229:, 221:, 211:39 209:, 193:, 185:, 175:29 173:, 121:. 36:. 362:e 355:t 348:v 337:. 305:e 298:t 291:v 280:. 225:: 217:: 189:: 181:: 115:H 98:0 95:= 90:x 87:x 83:u 79:H 76:+ 71:x 67:u 63:u 60:+ 55:t 51:u

Index

integro-differential equation
internal waves
Benjamin (1967)
Ono (1975)
Hilbert transform
Bretherton equation
Benjamin, T. Brooke
Bibcode
1967JFM....29..559B
doi
10.1017/s002211206700103x
S2CID
123065419
Bibcode
1975JPSJ...39.1082O
doi
10.1143/JPSJ.39.1082
MR
0398275
Benjamin-Ono equations: Solitons and Shock Waves
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applied mathematics
stub
expanding it
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e
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theoretical physics
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