Semi-rational solutions of the third-type Davey-Stewartson equation

Chaos - Tập 27 Số 8 - 2017
Jiguang Rao1,2, K. Porsezian3,4, Jingsong He1,2
12Department of Physics, Pondicherry University, Pondicherry 605014, India
2Department of Mathematics, Ningbo University 1 , Ningbo, Zhejiang 315211, People's Republic of China
31Department of Mathematics, Ningbo University, Ningbo, Zhejiang 315211, People's Republic of China
4Department of Physics, Pondicherry University 2 , Pondicherry 605014, India

Tóm tắt

General dark solitons and mixed solutions consisting of dark solitons and breathers for the third-type Davey-Stewartson (DS-III) equation are derived by employing the bilinear method. By introducing the two differential operators, semi-rational solutions consisting of rogue waves, breathers, and solitons are generated. These semi-rational solutions are given in terms of determinants whose matrix elements have simple algebraic expressions. Under suitable parametric conditions, we derive general rogue wave solutions expressed in terms of rational functions. It is shown that the fundamental (simplest) rogue waves are line rogue waves. It is also shown that the multi-rogue waves describe interactions of several fundamental rogue waves, which would generate interesting curvy wave patterns. The higher order rogue waves originate from a localized lump and retreat back to it. Several types of hybrid solutions composed of rogue waves, breathers, and solitons have also been illustrated. Specifically, these semi-rational solutions have a new phenomenon: lumps form on dark solitons and gradual separation from the dark solitons is observed.

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Tài liệu tham khảo

2008, Annu. Rev. Fluid Mech., 40, 287, 10.1146/annurev.fluid.40.111406.102203

2009, Phys. Lett. A, 373, 675, 10.1016/j.physleta.2008.12.036

2009, Phys. Today, 62, 62, 10.1063/1.3156339

2008, Extreme Ocean Waves

2010, Nonlinear Ocean Waves and the Inverse Scattering Transform

2009, Phys. Rev. A, 80, 033610, 10.1103/PhysRevA.80.033610

2010, Eur. Phys. J. Spec. Top., 185, 169, 10.1140/epjst/e2010-01247-6

2009, Phys. Rev. Lett., 103, 173901, 10.1103/PhysRevLett.103.173901

2007, Nature (London), 450, 1054, 10.1038/nature06402

2010, Phys. Rev. Lett., 104, 093901, 10.1103/PhysRevLett.104.093901

2008, Phys. Rev. Lett., 101, 065303, 10.1103/PhysRevLett.101.065303

2011, Phys. Plasmas, 18, 032301, 10.1063/1.3559486

2011, Phys. Rev. Lett., 107, 255005, 10.1103/PhysRevLett.107.255005

2017, Phys. Rev. E, 95, 042211, 10.1103/PhysRevE.95.042211

2015, J. Fluid Mech., 782, 25, 10.1017/jfm.2015.538

2007, Ocean Eng., 34, 1631, 10.1016/j.oceaneng.2006.11.006

2012, Phys. Rev. Lett., 108, 233901, 10.1103/PhysRevLett.108.233901

2011, Phys. Rev. Lett., 107, 274101, 10.1103/PhysRevLett.107.274101

1983, J. Aust. Math. Soc. B, 25, 16, 10.1017/S0334270000003891

2011, Nat. Hazards Earth. Syst. Sci., 11, 667, 10.5194/nhess-11-667-2011

2009, Phys. Rev. E, 80, 026601, 10.1103/PhysRevE.80.026601

2010, Eur. Phys. J. Spec. Top., 185, 247, 10.1140/epjst/e2010-01252-9

2011, Phys. Lett. A, 375, 2782, 10.1016/j.physleta.2011.05.047

2012, Phys. Rev. E, 85, 026607, 10.1103/PhysRevE.85.026607

2011, Phys. Rev. E, 84, 056611, 10.1103/PhysRevE.84.056611

2012, Proc. R. Soc. A, 468, 1716, 10.1098/rspa.2011.0640

2013, Phys. Rev. E, 87, 052914, 10.1103/PhysRevE.87.052914

2013, Phys. Rev. Lett., 111, 114101, 10.1103/PhysRevLett.111.114101

2015, Phys. Scr., 90, 105201, 10.1088/0031-8949/90/10/105201

2015, Opt. Express, 23, 349, 10.1364/OE.23.000349

2016, Nonlinear Anal. Real World Appl., 31, 179, 10.1016/j.nonrwa.2016.01.001

2013, Phys. Rev. E, 88, 023202, 10.1103/PhysRevE.88.023202

2012, Phys. Lett. A, 376, 1558, 10.1016/j.physleta.2012.03.032

2012, Phys. Rev. E, 86, 026606, 10.1103/PhysRevE.86.026606

2012, Phys. Rev. E, 85, 026601, 10.1103/PhysRevE.85.026601

2015, Lett. Math. Phys., 105, 853, 10.1007/s11005-015-0758-x

2014, Phys. Rev. E, 90, 033203, 10.1103/PhysRevE.90.033203

2015, SIAM J. Appl. Math., 75, 1, 10.1137/140963686

2014, Phys. Rev. E, 89, 041201, 10.1103/PhysRevE.89.041201

2014, Proc. R. Soc. A, 470, 0318, 10.1098/rspa.2014.0318

2016, Phys. Rev. E, 93, 012217, 10.1103/PhysRevE.93.012217

2017, Nonlinear Anal. Real World Appl., 33, 237, 10.1016/j.nonrwa.2016.06.006

2010, Phys. Rev. E, 82, 036610, 10.1103/PhysRevE.82.036610

2011, Phys. Lett. A, 375, 4274, 10.1016/j.physleta.2011.09.026

2015, Nonlinear. Dyn., 79, 2515, 10.1007/s11071-014-1829-8

2017, Commun. Nonlinear Sci. Numer. Simul., 45, 13, 10.1016/j.cnsns.2016.09.013

2017, Commun. Nonlinear Sci. Numer. Simul., 42, 699, 10.1016/j.cnsns.2016.06.015

2015, Commun. Nonlinear Sci. Numer. Simulat., 20, 434, 10.1016/j.cnsns.2014.06.012

2012, Phys. Rev. A, 85, 013828, 10.1103/PhysRevA.85.013828

2016, Opt. Express, 24, 15251, 10.1364/OE.24.015251

2016, Phys. Rev. Lett., 116, 173901, 10.1103/PhysRevLett.116.173901

2002, Opt. Lett., 27, 2182, 10.1364/OL.27.002182

2001, Phys. Rev. Lett., 87, 213902, 10.1103/PhysRevLett.87.213902

2001, Phys. Rev. Lett., 87, 043902, 10.1103/PhysRevLett.87.043902

1996, Phys. Rev. Lett., 77, 3783, 10.1103/PhysRevLett.77.3783

1999, Phys. Rev. Lett., 82, 4631, 10.1103/PhysRevLett.82.4631

2007, J. Nonlinear Sci., 17, 429, 10.1007/s00332-007-9001-y

2012, J. Nonlinear Sci., 22, 763, 10.1007/s00332-012-9127-4

1993, Inverse Prob., 9, 1, 10.1088/0266-5611/9/1/001

1992, Inverse Prob., 8, 263, 10.1088/0266-5611/8/2/007

1981, Phys. Rev. Lett., 47, 1096, 10.1103/PhysRevLett.47.1096

1994, Inverse Prob., 10, L19, 10.1088/0266-5611/10/2/002

1983, Theor. Math. Phys., 56, 720, 10.1007/BF01027548

1988, Commun. Math. Phys., 115, 375, 10.1007/BF01218017

1988, Commun. Math. Phys., 116, 449, 10.1007/BF01229203

2014, Nonlinear Anal. Real World Appl., 18, 1, 10.1016/j.nonrwa.2014.01.005

2012, Phys. Rev. E, 86, 036604, 10.1103/PhysRevE.86.036604

2013, J. Phys. A: Math. Theor., 46, 105202, 10.1088/1751-8113/46/10/105202

2015, Phys. Lett. A, 379, 1510, 10.1016/j.physleta.2015.02.040

Rogue Wave Solutions Zakharov Equation

2016, Rom. Rep. Phys., 68, 1425

2004, The Direct Method in Soliton Theory

2016, Chin. Phys. Lett., 33, 110201, 10.1088/0256-307X/33/11/110201

2011, Stud. Appl. Math., 127, 345, 10.1111/j.1467-9590.2011.00525.x

2001, Physica D, 152–153, 189, 10.1016/S0167-2789(01)00170-1

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Tập 27 Số 8

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