Solitons to rogue waves transition, lump solutions and interaction solutions for the (3+1)-dimensional generalized B-type Kadomtsev–Petviashvili equation in fluid dynamics

References

• H. Bailung, S.K. Sharma, and Y. Nakamura, Observation of Peregrine solitons in a multi component plasma with negative ions, Phys. Rev. Lett. 107 (2011), p. 255055. doi: 10.1103/PhysRevLett.107.255005
   Web of Science ®Google Scholar
• J. Chai, B. Tian, W.-R. Sun, and X.-Y. Xie, Solitons and rouge waves for a generalized (3+ 1)-dimensional variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics, Comput. Math. Appl. 71 (2016), pp. 2060–2068. doi: 10.1016/j.camwa.2016.03.022
   Web of Science ®Google Scholar
• Z. Du, B. Tian, H.-P. Chai, Y. Sun, and X.-H. Zhao, Rogue waves for the coupled variable-coefficient fourth-order nonlinear Schrödinger equations in an inhomogeneous optical fiber, Chaos Solitons Fractals 109 (2018), pp. 90–98. doi: 10.1016/j.chaos.2018.02.017
   Web of Science ®Google Scholar
• P. Dubard and V.B. Matveev, Multi-rogue waves solutions to the focusing NLS equation and the KP-I equation, Nat. Hazards Earth Syst. Sci. 11(3) (2011), pp. 667–672. doi: 10.5194/nhess-11-667-2011
   Web of Science ®Google Scholar
• P. Dubard and V.B. Matveev, Multi-rogue waves solutions: From the NLS to the KP-I equation, Nonlinearity 26(12) (2013), p. R93. doi: 10.1088/0951-7715/26/12/R93
   Web of Science ®Google Scholar
• J.M. Dudley, G. Genty, F. Dias, B. Kibler, and N. Akhmediev, Modulation instability, Akhmediev breathers and continuous wave supercontinuum generation, Opt. Express 17(24) (2009), pp. 21497–21508. doi: 10.1364/OE.17.021497
   PubMed Web of Science ®Google Scholar
• E. Falcon, C. Laroche, and S. Fauve, Observation of depression solitary surface waves on a thin fluid layer, Phys. Rev. Lett. 89 (2002), p. 204501. doi: 10.1103/PhysRevLett.89.204501
   PubMed Web of Science ®Google Scholar
• L.L. Feng and T.T. Zhang, Breather wave, rogue wave and solitary wave solutions of a coupled nonlinear Schrödinger equation, Appl. Math. Lett. 78 (2018), pp. 133–140. doi: 10.1016/j.aml.2017.11.011
   Web of Science ®Google Scholar
• P. Gaillard, Rational solutions to the KPI equation and multi rogue waves, Ann. Phys. 367 (2016), pp. 1–5. doi: 10.1016/j.aop.2016.01.013
   Web of Science ®Google Scholar
• X.Y. Gao, Bäcklund transformation and shock-wave-type solutions for a generalized (3+ 1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid mechanics, Ocean Eng. 96 (2015), pp. 245–247. doi: 10.1016/j.oceaneng.2014.12.017
   Web of Science ®Google Scholar
• X.Y. Gao, Looking at a nonlinear inhomogeneous optical fiber through the generalized higher-order variable-coefficient Hirota equation, Appl. Math. Lett. 73 (2017), pp. 143–149. doi: 10.1016/j.aml.2017.03.020
   Web of Science ®Google Scholar
• R. Hirota, The Direct Method in Soliton Theory, Cambridge University Press, Cambridge, 2004.
   Google Scholar
• Z.-Z. Lan, Y-T. Gao, J-W. Yang, C.-Q. Su, C. Zhao, and Z. Gao, Solitons and Bäcklund transformation for a generalized (3+1)-dimensional variable-coefficient B-type Kadomtsev-Petviashvili equation in fluid dynamics, Appl. Math. Lett. 60 (2016), pp. 96–100. doi: 10.1016/j.aml.2016.03.021
   Web of Science ®Google Scholar
• L. Liu, B. Tian, Y.-Q. Yuan, and Z. Du, Dark-bright solitons and semirational rogue waves for the coupled Sasa-Satsuma equations, Phys. Rev. E. 97 (2018), p. 052217.
   PubMed Web of Science ®Google Scholar
• H.C. Ma and A.P. Deng, Lump solution of (2+1)-dimensional Boussinesq equation, Commun. Theor. Phys. 65 (2016), pp. 546–552. doi: 10.1088/0253-6102/65/5/546
   Web of Science ®Google Scholar
• B.Y. Ohta and J. Yang, General high-order rogue waves and their dynamics in the nonlinear Schrödinger equation, Proc. R. Soc. A Math. Phys. Eng. Sci. 468 (2012), pp. 1716–1740. doi: 10.1098/rspa.2011.0640
   Web of Science ®Google Scholar
• Y. Ohta and J.K. Yang, Rogue waves in the Davey-Stewartson I equation, Phys. Rev. E 86 (2012), p. 036604.
   Web of Science ®Google Scholar
• Y. Ohta and J.K. Yang, Dynamics of rogue waves in the Davey-Stewartson II equation, J. Phys. A 46 (2013), p. 105202. doi: 10.1088/1751-8113/46/10/105202
   Google Scholar
• D.E. Pelinovsky, Y.A. Stepanyants, and Y.S. Kivshar, Self-focusing of plane dark solitons in nonlinear defocusing media, Phys. Rev. E 51 (1995), pp. 5016–5026. doi: 10.1103/PhysRevE.51.5016
   Web of Science ®Google Scholar
• V.I. Petiashvili and O.V. Pokhotelov, Solitary Waves in Plasmas and in the Atmosphere, Energoatomizdat, Moscow, 1989.
   Google Scholar
• C. Qian, J.G. Rao, Y.B. Liu, and J.-S. He, Rogue waves in the three-dimensional Kadomtsev-Petviashvili equation, Chin. Phys. Lett. 33(11) (2016), p. 110201. doi: 10.1088/0256-307X/33/11/110201
   Web of Science ®Google Scholar
• C.Y. Qin, S.F. Tian, X.B. Wang, T.T. Zhang, and J. Li, Rogue waves, bright-dark solitons and traveling wave solutions of the (3+1)-dimensional generalized Kadomtsev-Petviashvili equation, Comput. Math. Appl. 75(12) (2018), pp. 4221–4231. doi: 10.1016/j.camwa.2018.03.024
   Web of Science ®Google Scholar
• C.Y. Qin, S.F. Tian, L. Zou, and W.X. Ma, Solitary wave and quasi-periodic wave solutions to a (3+1)-dimensional generalized Calogero-Bogoyavlenskii-Schiff equation, Adv. Appl. Math. Mech. 10(4) (2018), pp. 948–977.
   Web of Science ®Google Scholar
• H.F. Shen and M.H. Tu, On the constrained B-type Kadomtsev-Petviashvili equation: Hirota bilinear equations and Virasoro symmetry, J. Math. Phys. 52 (2011), p. 032704. doi: 10.1063/1.3559081
   Web of Science ®Google Scholar
• D.R. Solli, C. Ropers, P. Koonath, and B. Jalali, Optical rogue waves, Nature. 450 (2007), pp. 1054–1057. doi: 10.1038/nature06402
   PubMed Web of Science ®Google Scholar
• M. Tajiri and T. Arai, Growing-and-decaying mode solution to the Davey-Stewartson equation, Phys. Rev. E 60 (1999), pp. 2297–2305. doi: 10.1103/PhysRevE.60.2297
   Web of Science ®Google Scholar
• S.F. Tian, Asymptotic behavior of a weakly dissipative modified two-component Dullin-Gottwald-Holm system, Appl. Math. Lett. 83 (2018), pp. 65–72. doi: 10.1016/j.aml.2018.03.019
   Web of Science ®Google Scholar
• S.F. Tian, Infinite propagation speed of a weakly dissipative modified two-component Dullin–Gottwald–Holm system, Appl. Math. Lett. 89 (2019), pp. 1–7. doi: 10.1016/j.aml.2018.09.010
   Web of Science ®Google Scholar
• S.F. Tian and H.Q. Zhang, On the integrability of a generalized variable-coefficient Kadomtsev-Petviashvili equation, J. Phys. A Math. Theor. 45 (2012), p. 055203.
   Web of Science ®Google Scholar
• S.F. Tian and H.Q. Zhang, On the integrability of a generalized variable-coefficient forced Korteweg-de Vries equation in fluids, Stud. Appl. Math. 132 (2014), pp. 212–246. doi: 10.1111/sapm.12026
   Web of Science ®Google Scholar
• S.F. Tian and T.T. Zhang, Long-time asymptotic behavior for the Gerdjikov-Ivanov type of derivative nonlinear Schrödinger equation with time-periodic boundary condition, Proc. Amer. Math. Soc. 146(4) (2018), pp. 1713–1729. doi: 10.1090/proc/13917
   Web of Science ®Google Scholar
• J.-M. Tu, S.-F. Tian, M.-J. Xu, P.-L. Ma, and T.-T. Zhang, On periodic wave solutions with asymptotic behaviors to a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid dynamics, Comput. Math. Appl. 72(9) (2016), pp. 2486–2504. doi: 10.1016/j.camwa.2016.09.003
   Web of Science ®Google Scholar
• J.M. Tu, S.F. Tian, M.J. Xu, and T.T. Zhang, Quasi-periodic waves and solitary waves to a generalized KdV-Caudrey-Dodd-Gibbon equation from fluid dynamics, Taiwanese J. Math. 20 (2016), pp. 823–848. doi: 10.11650/tjm.20.2016.6850
   Web of Science ®Google Scholar
• J. Villarroel, J. Prada, and P.G. Estévez, Dynamics of lump solutions in a 2+1 NLS equation, Stud. Appl. Math. 122 (2009), pp. 395–410. doi: 10.1111/j.1467-9590.2009.00440.x
   Web of Science ®Google Scholar
• X.B. Wang, S.F. Tian, and T.T. Zhang, Characteristics of the breather and rogue waves in a (2+1)-dimensional nonlinear Schrödinger equation, Proc. Amer. Math. Soc. 146(8) (2018), pp. 3353–3365. doi: 10.1090/proc/13765
   Web of Science ®Google Scholar
• X.B. Wang, S.F. Tian, L. Zou, and T.T. Zhang, Dynamics of solitary waves and periodic waves in a (3+1)-dimensional nonlinear evolution equation, East Asian J. Appl. Math. 8(3) (2018), pp. 477–497. doi:10.4208/eajam.221017.250218.
   Web of Science ®Google Scholar
• X.B. Wang, S.F. Tian, L.L. Feng, and T.T. Zhang, On quasi-periodic waves and rogue waves to the (4+1)-dimensional nonlinear Fokas equation, J. Math. Phys. 59(7) (2018), p. 073505. doi: 10.1063/1.5046691
   Web of Science ®Google Scholar
• X.B. Wang, T.T. Zhang, and M.J. Dong, Dynamics of the breathers and rogue waves in the higher-order nonlinear Schrödinger equation, Appl. Math. Lett. 86 (2018), pp. 298–304. doi: 10.1016/j.aml.2018.07.012
   Web of Science ®Google Scholar
• A.M. Wazwaz, Two B-type Kadomtsev-Petviashvili equations of (2+1) and (3+1) dimensions: Multiple soliton solutions, rational solutions and periodic solutions, Comput. Fluids. 86 (2013), pp. 357–362. doi: 10.1016/j.compfluid.2013.07.028
   Web of Science ®Google Scholar
• X.-Y. Wu, B. Tian, H.-P. Chai, and Y. Sun, Rogue waves and lump solutions for a (3+1)-dimensional generalized B-type Kadomtsev-Petviashvili equation in fluid mechanics, Mod. Phys. Lett. B. 31(22) (2017), p. 1750122. doi: 10.1142/S0217984917501226
   Web of Science ®Google Scholar
• X.-Y. Wu, B. Tian, L. Liu, and Y. Sun, Rogue waves for a variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics, Comput. Math. Appl. 72(2) (2018), pp. 215–223. doi: 10.1016/j.camwa.2017.12.021
   Google Scholar
• M.J. Xu, S.F. Tian, J.M. Tu, and T.T. Zhang, Bäcklund transformation, infinite conservation laws and periodic wave solutions to a generalized (2+1)-dimensional Boussinesq equation, Nonlinear Anal. RWA 31 (2016), pp. 388–408. doi: 10.1016/j.nonrwa.2016.01.019
   Web of Science ®Google Scholar
• X.W. Yan, S.F. Tian, M.J. Dong, L. Zhou, and T.T. Zhang, Characteristics of solitary wave, homoclinic breather wave and rogue wave solutions in a (2+1)-dimensional generalized breaking soliton equation, Comput. Math. Appl. 76(1) (2018), pp. 179–186. doi: 10.1016/j.camwa.2018.04.013
   Web of Science ®Google Scholar
• Y.-Q. Yuan, B. Tian, L. Liu, X.-Y. Wu, and Y. Sun, Solitons for the (2+1)-dimensional Konopelchenko-Dubrovsky equations, J. Math. Anal. Appl. 460 (2018), pp. 476–486. doi: 10.1016/j.jmaa.2017.11.024
   Web of Science ®Google Scholar
• X.-H. Zhao, B. Tian, J. Chai, X.-Y. Wu, and Y.-J. Guo, Multi-soliton interaction of a generalized Schrödinger-Boussinesq system in a magnetized plasma, Eur. Phys. J. Plus. 132 (2018), p. 192. doi: 10.1140/epjp/i2017-11453-5
   Web of Science ®Google Scholar