Further study of the localized solutions of the (2+1)-dimensional B-Kadomtsev-Petviashvili equation. (English) Zbl 1508.35133
Summary: In this paper, the localized solutions of the (2+1)-dimensional B-Kadomtsev-Petviashvili (BKP) equation, which is a useful physical model, are further studied. Firstly, by using the theory of Hirota bilinear operator, the corresponding N-soliton solutions are obtained. Then the localized solutions, which are the M-lump solutions, higher-order breathers and hybrid solutions, are also constructed by taking a long-wave limit and introducing some conjugation conditions. In the meanwhile, the dynamic behaviors of these obtained solutions are analyzed and shown graphically by the corresponding numerical simulations with specific parameters, which can greatly affect the solutions, such as the propagation properties.
MSC:
| 35Q53 | KdV equations (Korteweg-de Vries equations) |
| 35Q51 | Soliton equations |
| 37K10 | Completely integrable infinite-dimensional Hamiltonian and Lagrangian systems, integration methods, integrability tests, integrable hierarchies (KdV, KP, Toda, etc.) |
| 35C08 | Soliton solutions |
Keywords:
B-Kadomtsev-Petviashvili equation; M-lump solutions; higher-order breathers; hybrid solutionsReferences:
| [1] | Yang, J. Y.; Ma, W. X., Lump solutions to the BKP equation by symbolic computation, Internat J Modern Phys B, 30, Article 1640028 pp. (2016) · Zbl 1357.35080 |
| [2] | Tang, Y. N.; Chen, Y. N.; Wang, L., Wronskian and Grammian solutions for the (2+1)-dimensional BKP equation, Theor Appl Mech Lett, 4, Article 013011 pp. (2014) |
| [3] | Date, E.; Jimbo, M.; Kashiwara, M., Operator approach to the Kadomtsev-Petviashvili equation-transformation groups for soliton equations III, J Phys Soci Japan, 50, 3806-3812 (1981) · Zbl 0571.35099 |
| [4] | van de Led, Johan, The Adler-Shiota-van Moerbeke formula for the BKP hierarchy, J Math Phys, 36, 4940 (1995) · Zbl 0844.35109 |
| [5] | Chen, J.; Yu, J. P.; Ma, W. X., Interaction solutions of the first BKP equation, Modern Phys Lett B, 33, Article 1950191 pp. (2019) |
| [6] | Rudneva, D.; Zabrodin, A., Dynamics of poles of elliptic solutions to the BKP equation, J Phys A, 53, Article 075202 pp. (2020) · Zbl 1514.37090 |
| [7] | Hu, X. B.; Wang, H. Y., Construction of dKP and BKP equations with self-consistent sources, Inverse Probl, 22, 1903-1920 (2006) · Zbl 1105.37043 |
| [8] | Zhang, H. P.; Li, B.; Chen, Y., Full symmetry groups, painlevé integrability and exact solutions of the nonisospectral BKP equation, Appl Math Comput, 217, 1555-1560 (2010) · Zbl 1202.35281 |
| [9] | Satsuma, J.; Ablowitz, M. J., Two-dimensional lumps in nonlinear dispersive systems, J Math Phys, 20, 1496-1503 (1979) · Zbl 0422.35014 |
| [10] | 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 interactio, Phys Lett A, 63, 205-206 (1977) |
| [11] | Ma, W. X., Lump solutions to the KP equation, Phys Lett A, 379, 1975-1978 (2015) · Zbl 1364.35337 |
| [12] | 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 |
| [13] | Zhang, Y.; Liu, Y. P.; Tang, X. Y., M-lump solutions to a (3+1)-dimensional nonlinear evolution equation, Comput Math Appl, 76, 592-601 (2018) · Zbl 1420.35335 |
| [14] | Ma, W. X.; Qin, Z. Y.; Lü, X., Lump solutions to dimensionally reduced p-gkp and p-gbkp equations, Nonlinear Dynam, 84, 923-931 (2016) · Zbl 1354.35127 |
| [15] | Zhang, Y.; Dong, H. H.; Zhang, X. E.; Yang, H. W., Rational solutions and lump solutions to the generalized (3 + 1)- dimensional shallow water-like equation, Comput Math Appl, 73, 246-252 (2017) · Zbl 1368.35240 |
| [16] | 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 |
| [17] | Lou, S. Y.; Yu, J.; Weng, J. P.; Qian, X. M., Symmetry structure of (2 +1)-dimensionals bilinear Sawada-Kotera equations, Acta Phys Sininca, 43, 1050-1055 (1994) · Zbl 0835.35135 |
| [18] | Manukure, S.; Zhou, Y.; Ma, W. X., Lump solutions to a (2 + 1)-dimensional extended KP equation, Comput Math Appl, 7, 2414-2419 (2018) · Zbl 1409.35183 |
| [19] | Yue, Y. F.; Huang, L. L.; Chen, Y., N-solitons, breathers, lumps and rogue wave solutions to a (3 + 1)-dimensional nonlinear evolution equation, Comput Math Appl, 75, 2538-2548 (2018) · Zbl 1409.35188 |
| [20] | Ablowitz, M. J.; Clarkson, P. A., Solitons, nonlinear evolution equations and inverse scattering (1991), Cambridge University Press · Zbl 0762.35001 |
| [21] | Hirota, R., The direct method in soliton theory (2004), Cambridge University Press · Zbl 1099.35111 |
| [22] | Ma, W. X., Generalized bilinear differential equations, Stud Nonlinear Sci., 2, 140-144 (2011) |
| [23] | Ma, W. X.; Fan, E. G., Linear superposition principle applying to Hirota bilinear equations, Comput Math Appl, 61, 950-959 (2011) · Zbl 1217.35164 |
| [24] | Matveev, V. B.; Salle, M. A., Darboux transformations and solitons (1991), Springer · Zbl 0744.35045 |
| [25] | Zhaqilao, Z.; Li, B., Darboux transformation and various solutions for a nonlinear evolution equation in (3+1)-dimensions, Mod Phys Lett B, 22, 2945-2966 (2008) · Zbl 1175.35132 |
| [26] | Gu, C. H.; Hu, H. S.; Zhou, Z. X., Darboux transformation in soliton theory and its geometric applications (1999), Shanghai Scientific and Technical Publishers: Shanghai Scientific and Technical Publishers Shanghai |
| [27] | Rogers, C.; Schief, W. K., Bäcklund and Darboux transformations: Geometry and modern applications in soliton theory (2002), Cambridge University Press · Zbl 1019.53002 |
| [28] | 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) |
| [29] | Gelash, A. A.; Zakharov, V. E., Superregular solitonic solutions: a novel scenario for the nonlinear stage of modulation instability, Nonlinearity, 27, R1-R39 (2014) · Zbl 1343.37069 |
| [30] | An, H. L.; Feng, D. L.; Zhu, H. X., General M-lump, high-order breather and localized interaction solutions to the (2+1)-dimensional Sawada-Kotera equation, Nonlinear Dynam, 98, 1275-1286 (2019) |
| [31] | Wang, D. S.; Liu, J., Integrability aspects of some two-component KdV systems, Appl Math Lett, 79, 211-219 (2018) · Zbl 1461.37072 |
| [32] | Geng, X. G., Algebraic-geometrical solutions of some multidimensional nonlinear evolution equations, J Phys A: Math Gen, 36, 2289 (2003) · Zbl 1039.37061 |
| [33] | Wazwaz, A. M., A (3+1)-dimensional nonlinear evolution equation with multiple soliton solutions and multiple singular soliton solutions, Appl Math Comput, 215, 1548-1552 (2009) · Zbl 1179.35278 |
| [34] | Ren, B.; Cheng, X. P.; Lin, J., The (2+1)-dimensional Konopelchenko-Dubrovsky equation: nonlocal symmetries and interaction solutions, Nonlinear Dynam, 86, 1855-1862 (2016) · Zbl 1371.35004 |
| [35] | Wang, D. S.; Wang, X. L., Long-time asymptotics and the bright N-soliton solutions of the Kundu-Eckhaus equation via the Riemann-Hilbert approach, Nonlinear Anal RWA, 41, 334-361 (2018) · Zbl 1387.35056 |
| [36] | Yin, Y. H.; Ma, W. X.; Liu, J. G.; Lü, X., Diversity of exact solutions to a (3+1)-dimensional nonlinear evolution equation and its reduction, Comput Math Appl, 76, 1275-1283 (2018) · Zbl 1434.35172 |
| [37] | Wu, J. P.; Geng, X. G.; Zhang, L. L., N-soliton solution of a generalized hirota-satsuma coupled kdv equation and its reduction, Chin Phys Lett, 26, Article 020202 pp. (2009) |
| [38] | Ren, B., Interaction solutions for mKP equation with nonlocal symmetry reductions and CTE method, Phys Scr, Article 065206 pp. (2015) |
| [39] | Olver, P. J.; Rosenau, P., The construction of special solutions to partial differential equations, Phys Lett A, 114, 107-112 (1986) · Zbl 0937.35501 |
| [40] | Wang, D. S.; Shi, Y. R.; Feng, W. X.; Wen, L., Dynamical and energetic instabilities of \(F = 2\) spinor Bose-Einstein condensates in an optical lattice, Physica D, 351-352, 30-41 (2017) |
| [41] | He, J. S.; Zhang, H. R.; Wang, L. H.; Fokas, A. S., Generating mechanism for higher-order rogue waves, Phys Rev E, 87, Article 052914 pp. (2013) |
| [42] | Xu, G. Q., Painlevé classification of a generalized coupled Hirota system, Phys Rev E, 74, Article 027602 pp. (2006) |
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
