N-solitons, breathers and rogue waves for a generalized Boussinesq equation

References

• M.J. Ablowitz, D.J. Kaup, A.C. Newell, and H. Segur, Method for solving the sine-Gordon equation, Phys. Rev. Lett. 30 (1973), pp. 1262–1264. doi: 10.1103/PhysRevLett.30.1262
   Web of Science ®Google Scholar
• N.N. Akhmediev, V.M. Eleonskii, and N.E. Kulagin, First-order exact solutions of the nonlinear Schrödinger equation, Theor. Math. Phys. 72 (1987), pp. 809–818. doi: 10.1007/BF01017105
   Web of Science ®Google Scholar
• M.T. Darvishi, M. Najafi, and A.M. Wazwaz, Soliton solutions for Boussinesq-like equations with spatio-temporal dispersion, Ocean Eng. 130 (2017), pp. 228–240. doi: 10.1016/j.oceaneng.2016.11.052
   Web of Science ®Google Scholar
• M.J. Dong, S.F. Tian, X.W. Yan, and L. Zou, Solitary waves, homoclinic breather waves and rogue waves of the (3+1)-dimensional Hirota bilinear equation, Comput. Math. Appl. 75 (2018), pp. 957–964. doi: 10.1016/j.camwa.2017.10.037
   Web of Science ®Google Scholar
• X.X. Du, B. Tian, X.Y. Wu, H.M. Yin, and C.R. Zhang, Lie group analysis, analytic solutions and conservation laws of the (3+1)-dimensional Zakharov-Kuznetsov-Burgers equation in a collisionless magnetized electron-positron-ion plasma, Eur. Phys. J. Plus 133 (2018), p. 378. doi: 10.1140/epjp/i2018-12239-y
   Web of Science ®Google Scholar
• J.M. Dudley, F. Dias, M. Erkintalo, and G. Genty, Instabilities, breathers and rogue waves in optics, Nat. Photonics 8 (2014), pp. 755–764. doi: 10.1038/nphoton.2014.220
   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
• X.Y. Gao, Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas, Appl. Math. Lett. 91 (2019), pp. 165–172. doi: 10.1016/j.aml.2018.11.020
   Web of Science ®Google Scholar
• W.Y. Guan and B.Q. Li, New observation on the breather for a generalized nonlinear Schrödinger system with two higher-order dispersion operators in inhomogeneous optical fiber, Optik 181 (2019), pp. 853–861. doi: 10.1016/j.ijleo.2018.12.148
   Web of Science ®Google Scholar
• R. Guo, H.H. Zhao, and Y. Wang, A higher-order coupled nonlinear Schrödinger system: Solitons, breathers, and rogue wave solutions, Nonlinear Dyn. 83 (2016), pp. 2475–2484. doi: 10.1007/s11071-015-2495-1
   Web of Science ®Google Scholar
• C.C. Hu, B. Tian, X.Y. Wu, Y.Q. Yuan, and Z. Du, Mixed lump-kink and rogue wave-kink solutions for a (3+1)-dimensional B-type Kadomtsev-Petviashvili equation in fluid mechanics, Eur. Phys. J. Plus 133 (2018), p. 40. doi: 10.1140/epjp/i2018-11875-5
   Web of Science ®Google Scholar
• M. Inc, New solitary wave solutions with compact support and Jacobi elliptic function solutions for the nonlinearity dispersive Boussinesq equations, Chaos Solitons Fract. 37 (2008), pp. 792–798. doi: 10.1016/j.chaos.2006.09.064
   Web of Science ®Google Scholar
• E.A. Kuznetsov, Solitons in a parametrically unstable plasma, Sov. Phys.-Dokl. (Engl. Transl.) 22 (1977), pp. 507–508.
   Google Scholar
• B.Q. Li and Y.L. Ma, The multiple-lump waves for a (3+1)-dimensional Boiti-Leon-Manna-Pempinelli equation arising from incompressible fluid, Comput. Math. Appl. 76 (2018), pp. 204–214. doi: 10.1016/j.camwa.2018.04.015
   Web of Science ®Google Scholar
• C. Liu, Z.Y. Yang, L.C. Zhao, L. Duan, G.Y. Yang, and W.L. Yang, Symmetric and asymmetric optical multipeak solitons on a continuous wave background in the femtosecond regime, Phys. Rev. E 94 (2016), p. 042221.
   PubMed Web of Science ®Google Scholar
• C. Liu, Y. Ren, Z.Y. Yang, and W.L. Yang, Superregular breathers in a complex modified Korteweg-de Vries system, Chaos 27 (2017), pp. 083120.
   PubMed Web of Science ®Google Scholar
• C. Liu, Z.Y. Yang, and W.L. Yang, Growth rate of modulation instability driven by superregular breathers, Chaos 28 (2018), p. 083110.
   PubMed Web of Science ®Google Scholar
• C. Liu, Z.Y. Yang, W.L. Yang, and N. Akhmediev, Chessboard-like spatio-temporal interference patterns and their excitation, J. Opt. Soc. Am. B 36 (2019), pp. 1294–1299. doi: 10.1364/JOSAB.36.001294
   Web of Science ®Google Scholar
• Y.C. Ma, The perturbed plane-wave solutions of the cubic Schrödinger equation, Stud. Appl. Math. 60 (1979), pp. 43–58. doi: 10.1002/sapm197960143
   Web of Science ®Google Scholar
• Y.L. Ma and B.Q. Li, Analytic rogue wave solutions for a generalized fourth-order Boussinesq equation in fluid mechanics, Math. Methods Appl. Sci. 42 (2019), pp. 39–48. doi: 10.1002/mma.5320
   Web of Science ®Google Scholar
• W.X. Ma, C.X. Li, and J.S. He, A second Wronskian formulation of the Boussinesq equation, Nonlinear Anal. Theory Methods Appl. 70 (2008), pp. 4245–4258. doi: 10.1016/j.na.2008.09.010
   Web of Science ®Google Scholar
• D.H. Peregrine, Long wave on a beach, J. Fluid Mech. 27 (1967), pp. 815–827. doi: 10.1017/S0022112067002605
   Web of Science ®Google Scholar
• S.S. Ray, A novel method for travelling wave solutions of fractional Whitham-Broer-Kaup, fractional modified Boussinesq and fractional approximate long wave equations in shallow water, Math. Methods Appl. Sci. 38 (2015), pp. 1352–1368. doi: 10.1002/mma.3267
   Web of Science ®Google Scholar
• Y. Ren, X. Wang, C. Liu, Z.Y. Yang, and W.L. Yang, Characteristics of fundamental and superregular modes in a multiple self-induced transparency system, Commun. Nonlinear Sci. Numer. Simul. 63 (2018), pp. 161–170. doi: 10.1016/j.cnsns.2018.03.011
   Web of Science ®Google Scholar
• Y. Ren, C. Liu, Z.Y. Yang, and W.L. Yang, Polariton superregular breathers in a resonant erbium-doped fiber, Phys. Rev. E 98 (2018), pp. 062223.
   Web of Science ®Google Scholar
• F. Tchier, A.I. Aliyu, A. Yusuf, and M. Inc, Dynamics of solitons to the ill-posed Boussinesq equation, Eur. Phys. J. Plus 132 (2017), p. 136. doi: 10.1140/epjp/i2017-11430-0
   Web of Science ®Google Scholar
• A.M. Wazwaz, Solitons and singular solitons for a variety of Boussinesq-like equations, Ocean Eng. 53 (2012), pp. 1–5. doi: 10.1016/j.oceaneng.2012.06.012
   Web of Science ®Google Scholar
• A.M. Wazwaz, Multiple soliton solutions for an integrable couplings of the Boussinesq equation, Ocean Eng. 73 (2013), pp. 38–40. doi: 10.1016/j.oceaneng.2013.08.004
   Web of Science ®Google Scholar
• A.M. Wazwaz, Gaussian solitary waves for the logarithmic Boussinesq equation and the logarithmic regularized Boussinesq equation, Ocean Eng. 94 (2015), pp. 111–115. doi: 10.1016/j.oceaneng.2014.11.024
   Web of Science ®Google Scholar
• A.M. Wazwaz, Multiple soliton solutions and multiple complex soliton solutions for two distinct Boussinesq equations, Nonlinear Dyn. 85 (2016), pp. 731–737. doi: 10.1007/s11071-016-2718-0
   Web of Science ®Google Scholar
• X.T. Wu, B. Tian, L. Liu, and Y. Sun, Rogue waves for a variable-coefficient Kadomtsev-Petviashvili equation in fluid mechanics, Comput. Math. Appl. 76 (2018), pp. 215–223. doi: 10.1016/j.camwa.2017.12.021
   Web of Science ®Google Scholar
• X.W. Yan, S.F. Tian, J.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 (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
• V.E. Zakharov and A.A. Gelash, Nonlinear stage of modulation instability, Phys. Rev. Lett. 111 (2013), p. 054101. doi: 10.1103/PhysRevLett.111.054101
   PubMed Web of Science ®Google Scholar
• E.M.E. Zayed and A.G. Al-Nowehy, Solitons and other exact solutions for variant nonlinear Boussinesq equations, Optik 139 (2017), pp. 166–177. doi: 10.1016/j.ijleo.2017.03.092
   Web of Science ®Google Scholar
• C.R. Zhang, B. Tian, X.Y. Wu, Y.Q. Yuan, and X.X. Du, Rogue waves and solitons of the coherently-coupled nonlinear Schrödinger equations with the positive coherent coupling, Phys. Scr. 93 (2018), p. 095202. doi: 10.1088/1402-4896/aacfc6
   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 (2017), p. 192. doi: 10.1140/epjp/i2017-11453-5
   Web of Science ®Google Scholar
• X.H. Zhao, B. Tian, X.Y. Xie, X.Y. Wu, Y. Sun, and Y.J. Guo, Solitons, Backlund transformation and Lax pair for a (2+1)-dimensional Davey-Stewartson system on surface waves of finite depth, Waves Random Complex Media 28 (2018), pp. 356–366. doi: 10.1080/17455030.2017.1348645
   Web of Science ®Google Scholar