Characteristics of the lumps and stripe solitons with interaction phenomena in the \((2 + 1)\)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation. (English) Zbl 1415.37094
Summary: So far, the interaction between the lump waves and solitons has received much attention from many fields because of its significance to represent new physical phenomena occurring in various branches of physics. In this work, we study the interaction phenomenon between the lump waves and stripe solitons in the (2+1)-dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation by making use of the Hirota bilinear method. Adopting the positive quadratic function solutions of the corresponding bilinear equation, a class of lump wave solutions are analytically constructed. What is more, we obtain the lump-single stripe soliton interaction solutions, and show that the one stripe soliton can split into a lump and a stripe soliton. In addition, we provide the interaction solutions between one lump and twin resonance stripe solitons, and present the law of the interaction between a lump and twin resonance stripe solitons by the related three-dimensional plots.
MSC:
| 37K40 | Soliton theory, asymptotic behavior of solutions of infinite-dimensional Hamiltonian systems |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35C07 | Traveling wave solutions |
References:
| [1] | Leblond, H., Manna, M.: Single-oscillation two-dimensional solitons of magnetic polaritons. Phys. Rev. Lett. 99, 064102 (2007) · doi:10.1103/PhysRevLett.99.064102 |
| [2] | Leblond, H., Kremer, D., Mihalache, D.: Ultrashort spatiotemporal optical solitons in quadratic nonlinear media: generation of line and lump solitons from few-cycle input pulses. Phys. Rev. A. 80, 053812 (2009) · doi:10.1103/PhysRevA.80.053812 |
| [3] | Yang, C., Li, W., Yu, W., Liu, M., Zhang, Y., Ma, G., Lei, M., Liu, W.: Amplification, reshaping, fission and annihilation of optical solitons in dispersion-decreasing fiber. Nonlinear Dynam. 92, 203-213 (2018) · Zbl 1398.35013 · doi:10.1007/s11071-018-4049-9 |
| [4] | Lin, F.H., Chen, S.T., Qu, Q.X., Wang, J.P., Zhou, X.W., Lü, X.: Resonant multiple wave solutions to a new (3+1)-dimensional generalized Kadomtsev-Petviashvili equation: linear superposition principle. Appl. Math. Lett. 78, 112-117 (2018) · Zbl 1383.35193 · doi:10.1016/j.aml.2017.10.013 |
| [5] | Liu, W., Yang, C., Liu, M., Yu, W., Zhang, Y., Lei, M.: Effect of high-order dispersion on three-soliton interactions for the variable-coefficients Hirota equation. Phys. Rev. E. 96, 042201 (2017) · doi:10.1103/PhysRevE.96.042201 |
| [6] | Lü, X., Chen, S.T., Ma, W.X.: Constructing lump solutions to a generalized Kadomtsev-Petviashvili-Boussinesq equation. Nonlinear Dynam. 86, 523-534 (2016) · Zbl 1349.35007 · doi:10.1007/s11071-016-2905-z |
| [7] | Sun, W.R.: Breather-to-soliton transitions and nonlinear wave interactions for the nonlinear Schrödinger equation with the sextic operators in optical fibers. Ann. Phys. 529, 1600227 (2017) · Zbl 1357.35260 · doi:10.1002/andp.201600227 |
| [8] | Li, W.Y., Ma, G.L., Yu, W.T., Zhang, Y.J., Liu, M.L., Yang, C.Y., Liu, W.J.: Soliton structures in the (1+1)-dimensional Ginzburg-Landau equation with a parity-time-symmetric potential in ultrafast optics. Chinese Phys. B. 27, 030504 (2018) · doi:10.1088/1674-1056/27/3/030504 |
| [9] | Lü, X., Lin, F.: Soliton excitations and shape-changing collisions in alpha helical proteins with interspine coupling at higher order. Commun. Nonlinear Sci. Numer. Simul. 32, 241-261 (2016) · Zbl 1510.35309 · doi:10.1016/j.cnsns.2015.08.008 |
| [10] | Cai, L.Y., Wang, X., Wang, L., Li, M., Liu, Y., Shi, Y.Y.: Nonautonomous multi-peak solitons and modulation instability for a variable-coefficient nonlinear Schrödinger equation with higher-order effects. Nonlinear Dynam. 90, 2221-2230 (2017) · doi:10.1007/s11071-017-3797-2 |
| [11] | Gao, L.N., Zi, Y.Y., Yin, Y.H., Ma, W.X., Lü, X.: Bäcklund transformation, multiple wave solutions and lump solutions to a (3+1)-dimensional nonlinear evolution equation. Nonlinear Dynam. 89, 2233-2240 (2017) · doi:10.1007/s11071-017-3581-3 |
| [12] | Mertens, F.G., Quintero, N.R., Cooper, F., Khare, A., Saxena, A.: Nonlinear Dirac equation solitary waves in external fields. Phys. Rev. E. 86, 046602 (2012) · doi:10.1103/PhysRevE.86.046602 |
| [13] | Liu, M.L., Liu, W.J., Pang, L.H., Teng, H., Fang, S.B., Wei, Z.Y.: Ultrashort pulse generation in model-locked erbium-doped fiber lasers with tungsten disulfide saturable absorber. Opt. Commun. 406, 72-75 (2018) · doi:10.1016/j.optcom.2017.04.021 |
| [14] | Tomizawa, S., Mishima, T.: New cylindrical gravitational soliton waves and gravitational Faraday rotation. Phys. Rev. D. 90, 044036 (2014) · doi:10.1103/PhysRevD.90.044036 |
| [15] | Lü, X., Ma, W.X.: Soliton structures in the (1+1)-dimensional Ginzburg-Landau equation with a parity-time-symmetric potential in ultrafast optics. Nonlinear Dynam. 85, 1217-1222 (2016) · Zbl 1355.35159 · doi:10.1007/s11071-016-2755-8 |
| [16] | Hoefer, M.A., Sommacal, M., Silva, T.J.: Propagation and control of nanoscale magnetic-droplet solitons. Phys. Rev. B. 85, 214433 (2012) · doi:10.1103/PhysRevB.85.214433 |
| [17] | Solli, D.R., Ropers, C., Koonath, P., Jalali, B.: Optical rogue waves. Nature. 450, 1054-1057 (2007) · doi:10.1038/nature06402 |
| [18] | Zhang, J.H., Wang, L., Liu, C.: Superregular breathers, characteristics of nonlinear stage of modulation instability induced by higher-order effects. Proc. R. Soc. A. 473, 20160681 (2017) · Zbl 1404.35398 · doi:10.1098/rspa.2016.0681 |
| [19] | Wang, L., Zhu, Y.J., Wang, Z.Q., Xu, T., Qi, F.H., Xue, Y.S.: Asymmetric rogue waves, breather-to-soliton conversion, and nonlinear wave interactions in the Hirota-Maxwell-Bloch system. J. Phys. Soc. Jpn. 85, 024001 (2016) · doi:10.7566/JPSJ.85.024001 |
| [20] | Liu, W.J., Liu, M.L., Han, H.N., Fang, S.B., Teng, H., Lei, M., Wei, Z.Y.: Nonlinear optical properties of WSe2 and MoSe2 films and their applications in passively Q-switched erbium doped fiber lasers [invited]. Photonics. Res. 6, C15-C21 (2018) · doi:10.1364/PRJ.6.000C15 |
| [21] | Wang, L., Zhu, Y.J., Wang, Z.Z., Qi, F.H., Guo, R.: Higher-order semirational solutions and nonlinear wave interactions for a derivative nonlinear Schrödinger equation. Commun. Nonlinear Sci. Numer. Simul. 33, 218-228 (2016) · Zbl 1510.35314 · doi:10.1016/j.cnsns.2015.08.027 |
| [22] | Wang, L., Zhu, Y.J., Qi, F.H., Li, M., Guo, R.: Modulational instability, higher-order localized wave structures, and nonlinear wave interactions for a nonautonomous Lenells-Fokas equation in inhomogeneous fibers. Chaos. 25, 063111 (2015) · doi:10.1063/1.4922025 |
| [23] | Wang, L., Li, X., Qi, F.H., Zhang, L.L.: Breather interactions and higher-order nonautonomous rogue waves for the inhomogeneous nonlinear Schrödinger Maxwell-Bloch equations. Ann. Phys. 359, 97 (2015) · Zbl 1343.35056 · doi:10.1016/j.aop.2015.04.025 |
| [24] | Wang, L., Wu, X., Zhang, H.Y.: Superregular breathers and state transitions in a resonant erbium-doped fiber system with higher-order effects. Phys. Lett. A. 382, 2650-2654 (2018) · doi:10.1016/j.physleta.2018.07.036 |
| [25] | Li, P., Wang, L., Kong, L.Q., Wang, X., Xie, Z.Y.: Nonlinear waves in the modulation instability regime for the ffth-order nonlinear Schrödinger equation. Appl. Math. Lett. 85, 110-117 (2018) · Zbl 1405.35197 · doi:10.1016/j.aml.2018.05.027 |
| [26] | Liu, W.J., Liu, M.L., Ou Yang, Y.Y., Hou, H.R., Ma, G.L., Lei, M., Wei, Z.Y.: Tungsten diselenide for mode-locked erbium-doped fiber lasers with short pulse duration. Nanotechnology. 29, 174002 (2018) · doi:10.1088/1361-6528/aaae40 |
| [27] | Wang, L., Li, M., Qi, F.H., Xu, T.: Modulational instability, nonautonomous breathers and rogue waves for a variable-coefficient derivative nonlinear Schrödinger equation in the inhomogeneous plasmas. Phys. Plasmas. 22, 032308 (2015) · doi:10.1063/1.4915516 |
| [28] | Liu, W.J., Zhu, Y.N., Liu, M.L., Wen, B., Fang, S.B., Teng, H., Lei, M., Liu, L.M., Wei, Z.Y.: Optical properties and applications for MoS2-Sb2Te3-MoS2 heterostructure materials. Photonics. Res. 6, 220-227 (2018) · doi:10.1364/PRJ.6.000220 |
| [29] | Sun, W.R., Wang, L.: Matter rogue waves for the three-component Gross-Pitaevskii equations in the spinor Bose-Einstein condensates. Proc. R. Soc. A. 474, 20170276 (2018) · Zbl 1402.76165 · doi:10.1098/rspa.2017.0276 |
| [30] | Wang, L., Liu, C., Wu, X., Wang, X., Sun, W.R.: Dynamic of superregular breathers in the quintic nonlinear Schrödinger equation. Nonlinear Dynam. 94, 977-989 (2018). https://doi.org/10.1007/s11071-018-4404-x |
| [31] | Wang, L., Jiang, D.Y., Qi, F.H., Shi, Y.Y., Zhao, Y.C.: Dynamics of the higher-order rogue waves for a generalized mixed nonlinear Schrödinger model. Commun. Nonlinear Sci. Numer. Simul. 42, 502 (2017) · Zbl 1473.76016 · doi:10.1016/j.cnsns.2016.06.011 |
| [32] | Wang, L., Wang, Z.Q., Sun, W.R., Shi, Y.Y., Li, M., Xu, M.: Dynamics of Peregrine combs and Peregrine walls in an inhomogeneous Hirota and Maxwell-Bloch system. Commun. Nonlinear Sci. Numer. Simul. 47, 190 (2017) · Zbl 1510.35325 · doi:10.1016/j.cnsns.2016.11.009 |
| [33] | Kedziora, D.J., Ankiewicz, A., Akhmediev, N.: Classifying the hierarchy of nonlinear-Schrödinger-equation rogue-wave solutions. Phys. Rev. E. 88, 013207 (2013) · doi:10.1103/PhysRevE.88.013207 |
| [34] | He, J., Wang, L., Li, L., Porsezian, K., Erdélyi, R.: Few-cycle optical rogue waves: Complex modified Korteweg-de Vries equation. Phys. Rev. E. 89, 062917 (2014) · doi:10.1103/PhysRevE.89.062917 |
| [35] | Wang, L.H., Porsezian, K., He, J.S.: Breather and rogue wave solutions of a generalized nonlinear Schrödinger equation. Phys. Rev. E. 87, 053202 (2013) · doi:10.1103/PhysRevE.87.053202 |
| [36] | Sun, W.R., Liu, D.Y., Xie, X.Y.: Vector semirational rogue waves and modulation instability for the coupled higher-order nonlinear Schrödinger equations in the birefringent optical fibers. Chaos. 27, 043114 (2017) · Zbl 1390.35340 · doi:10.1063/1.4981907 |
| [37] | Manakov, S.V., Zakharov, V.E., Bordag, L.A., Its, A.R., Matveev, V.B.: Two-dimensional solitons of the Kadomtsev-Petviashvili equation and their interaction. Phys. Lett. A. 63, 205-206 (1977) · doi:10.1016/0375-9601(77)90875-1 |
| [38] | Estévez, P.G., Díaz, E., Domínguez-Adame, F., Cerveró, J.M., Diez, E.: Lump solitons in a higher-order nonlinear equation in 2 + 1 dimensions. Phys. Rev. E. 93, 062219 (2016) · doi:10.1103/PhysRevE.93.062219 |
| [39] | Lou, S.-Y.: On the coherent structures of the Nizhnik-Novikov-Veselov equation. Phys. Lett. A. 277, 94-100 (2000) · Zbl 1273.35264 · doi:10.1016/S0375-9601(00)00699-X |
| [40] | Ma, W.-X.: Lump solutions to the Kadomtsev-Petviashvili equation. Phys. Lett. A. 379, 1975-1978 (2015) · Zbl 1364.35337 · doi:10.1016/j.physleta.2015.06.061 |
| [41] | Satsuma, J., Ablowitz, M.J.: Two-dimensional lumps in nonlinear dispersive systems. J. Math. Phys. 20, 1496-1503 (1979) · Zbl 0422.35014 · doi:10.1063/1.524208 |
| [42] | Ma, W.X., Qin, Z.Y., Xing, L.: Lump solutions to dimensionally reduced p-gKP and p-gBKP equations. Nonlinear Dynam. 84, 923-931 (2016) · Zbl 1354.35127 · doi:10.1007/s11071-015-2539-6 |
| [43] | Huang, L.-L., Chen, Y.: Lump solutions and interaction phenomenon for (2+1) -dimensional Sawada-Kotera equation. Commun. Theor. Phys. 67, 473-478 (2017) · Zbl 1365.35137 · doi:10.1088/0253-6102/67/5/473 |
| [44] | Wang, H.: Lump and interaction solutions to the (2 + 1)-dimensional burgers equation. Appl. Math. Lett. 85, 27-34 (2018) · Zbl 1524.35558 · doi:10.1016/j.aml.2018.05.010 |
| [45] | Konopelchenko, B.G., Dubrovsky, V.G.: Some new Integrable nonlinear evolution equations in (2+1)-dimensions. Phys. Lett. A. 102, 15-17 (1984) · doi:10.1016/0375-9601(84)90442-0 |
| [46] | Cao, C.W., Wu, Y.T., Geng, X.G.: On quasi-periodic solutions of the 2+1 dimensional Caudrey-Dodd-Gibbon-Kotera-Sawada equation. Phys. Lett. A. 256, 59-65 (1999) · doi:10.1016/S0375-9601(99)00201-7 |
| [47] | Wang, L., Xian, D.: Homoclinic breather-wave solutions,periodic-wave solutions and kink solitary-wave solutions for CDGKS equations. Chin. J. Quantum Elect. 29, 417-420 (2012) |
| [48] | Meng, X.H.: The periodic solitary wave solutions for the (2+1)-dimensional fifth-order KdV equation. J. Appl. Math. Phys. 2, 639-643 (2014) · doi:10.4236/jamp.2014.27070 |
| [49] | Gao, L.-N., Zhao, X.-Y., Zi, Y.-Y., Yu, J., Lü, X.: Resonant behavior of multiple wave solutions to a Hirota bilinear equation. Computers and Mathematics with Applications. 72, 1225-1229 (2016) · Zbl 1361.35155 · doi:10.1016/j.camwa.2016.06.008 |
| [50] | Yang, J.-Y., Ma, W.-X.: Lump solutions to the BKP equation by symbolic computation. Int. J. Mod. Phys. B. 30, 1640028 (2016) · Zbl 1357.35080 · doi:10.1142/S0217979216400282 |
| [51] | Hossen, M.B., Roshida, H.-O., Ali, M.Z.: Characteristics of the solitary waves and rogue waves with interaction phenomena in a (2 +1)-dimensional breaking soliton equation. Phys. Lett. A. 352, 1268-1274 (2018) · doi:10.1016/j.physleta.2018.03.016 |
| [52] | Yang, H.W., Chen, X., Guo, M., Chen, Y.D.: A new ZK-BO equation for three-dimensional algebraic Rossby solitary waves and its solution as well as fission property. Nonlinear Dynam. 91, 2019-2032 (2018) · Zbl 1390.76044 · doi:10.1007/s11071-017-4000-5 |
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