Osman, M. S. Multi-soliton rational solutions for quantum Zakharov-Kuznetsov equation in quantum magnetoplasmas. (English) Zbl 1365.35012 Waves Random Complex Media 26, No. 4, 434-443 (2016). Summary: In this paper, the multi-soliton rational solutions are obtained for quantum Zakharov-Kuznetsov equation in quantum magnetoplasmas via the generalised unified method. Compared with the Hirota’s method and the inverse scattering method, the proposed method gives more general exact multi-wave solutions without much extra effort. The obtained results show that the generalised unified method provides a powerful mathematical tool for solving many nonlinear evolution equations arising in different branches of science. To give more physical insights into the obtained solutions, we present graphically their representative structures by setting the parameter \(H_e\) which is proportional to the ratio of the strength of magnetic field \(H_0\) to the electronic Fermi temperature \(T_{Fe}\) in the solutions of the quantum Zakharov-Kuznetsov equation as specific values. Cited in 17 Documents MSC: 35C08 Soliton solutions 35Q51 Soliton equations 76W05 Magnetohydrodynamics and electrohydrodynamics 35Q40 PDEs in connection with quantum mechanics 81Q80 Special quantum systems, such as solvable systems Keywords:generalised unified method; nonlinear evolution equation; multiple-solitary wave solutions PDFBibTeX XMLCite \textit{M. S. Osman}, Waves Random Complex Media 26, No. 4, 434--443 (2016; Zbl 1365.35012) Full Text: DOI References: [1] DOI: 10.1016/j.nonrwa.2011.12.001 · Zbl 1253.35143 · doi:10.1016/j.nonrwa.2011.12.001 [2] DOI: 10.1016/j.aml.2015.03.019 · Zbl 1326.35014 · doi:10.1016/j.aml.2015.03.019 [3] DOI: 10.1016/j.cnsns.2012.01.010 · Zbl 1248.35180 · doi:10.1016/j.cnsns.2012.01.010 [4] DOI: 10.1016/j.amc.2012.06.076 · Zbl 1291.35270 · doi:10.1016/j.amc.2012.06.076 [5] DOI: 10.1103/PhysRevLett.19.1095 · doi:10.1103/PhysRevLett.19.1095 [6] Gu C, NASA STI/Recon Technical Report A 1 (1995) [7] DOI: 10.1017/CBO9780511623998 · doi:10.1017/CBO9780511623998 [8] DOI: 10.1103/PhysRevLett.27.1192 · Zbl 1168.35423 · doi:10.1103/PhysRevLett.27.1192 [9] DOI: 10.1063/1.527815 · Zbl 0641.35073 · doi:10.1063/1.527815 [10] DOI: 10.1063/1.527421 · Zbl 0658.35081 · doi:10.1063/1.527421 [11] DOI: 10.1016/j.amc.2007.01.056 · Zbl 1243.35148 · doi:10.1016/j.amc.2007.01.056 [12] DOI: 10.1140/epjp/i2015-15215-1 · doi:10.1140/epjp/i2015-15215-1 [13] DOI: 10.1016/j.jare.2014.02.004 · doi:10.1016/j.jare.2014.02.004 [14] DOI: 10.7566/JPSJ.82.044004 · doi:10.7566/JPSJ.82.044004 [15] DOI: 10.1007/s13226-014-0047-x · Zbl 1307.35251 · doi:10.1007/s13226-014-0047-x [16] DOI: 10.1007/s12648-013-0248-x · doi:10.1007/s12648-013-0248-x [17] DOI: 10.1063/1.4856735 · doi:10.1063/1.4856735 [18] DOI: 10.1515/ijnsns-2012-0154 · Zbl 1401.82037 · doi:10.1515/ijnsns-2012-0154 [19] DOI: 10.1088/0031-8949/85/02/025006 · Zbl 1282.35323 · doi:10.1088/0031-8949/85/02/025006 [20] DOI: 10.1103/PhysRevE.79.056401 · doi:10.1103/PhysRevE.79.056401 [21] DOI: 10.1103/PhysRevLett.17.996 · doi:10.1103/PhysRevLett.17.996 [22] DOI: 10.1063/1.2750649 · doi:10.1063/1.2750649 [23] DOI: 10.1140/epjd/e2010-10342-5 · doi:10.1140/epjd/e2010-10342-5 [24] Elwakil SA, Chin. J. Phys 49 pp 732– (2011) [25] DOI: 10.1016/j.amc.2010.05.074 · Zbl 1200.35238 · doi:10.1016/j.amc.2010.05.074 [26] DOI: 10.3103/S1541308X11020117 · doi:10.3103/S1541308X11020117 [27] DOI: 10.1007/s10509-012-1072-z · Zbl 1284.81112 · doi:10.1007/s10509-012-1072-z 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.