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Analysis of fractional Kundu-Eckhaus and massive Thirring equations using a hybridization scheme. (English) Zbl 1518.35642

MSC:

35R11 Fractional partial differential equations
35A22 Transform methods (e.g., integral transforms) applied to PDEs

References:

[1] Wang, Y.; An, J.-Y., Amplitude-frequency relationship to a fractional duffing oscillator arising in microphysics and tsunami motion, Journal of Low Frequency Noise, Vibration and Active Control, 38, 3-4, 1008-1012 (2019) · doi:10.1177/1461348418795813
[2] Abdo, M. S.; Panchal, S. K., Fractional integro-differential equations involving \(\psi \)-Hilfer fractional derivative, Advances in Applied Mathematics and Mechanics, 11, 2, 338-359 (2019) · Zbl 1488.45022
[3] Sedighi, H. M.; Daneshmand, F., Static and dynamic pull-in instability of multi-walled carbon nanotube probes by Hes iteration perturbation method, Journal of Mechanical Science and Technology, 28, 9, 3459-3469 (2014) · doi:10.1007/s12206-014-0807-x
[4] Kundu, A., Landau-Lifshitz and higher-order nonlinear systems gauge generated from nonlinear Schrödinger-type equations, Journal of Mathematical Physics, 25, 12, 3433-3438 (1984) · doi:10.1063/1.526113
[5] Eckhaus, W., The Long-Time Behaviour for Perturbed Wave-Equations and Relatedproblems, Trends in Applications of Pure Mathematics to Mechanics, 168-194 (1986), Springer · Zbl 0629.35085 · doi:10.1007/BFb0016391
[6] Korepin, V. E., Direct calculation of the S matrix in the massive Thirring model, Teoreticheskaya Matematicheskaya Fizika, 41, 2, 953-967 (1979) · doi:10.1007/BF01028501
[7] Thirring, W. E., A soluble relativistic field theory, Annals of Physics, 3, 1, 91-112 (1958) · Zbl 0078.44303 · doi:10.1016/0003-4916(58)90015-0
[8] Feng, Z.; Wang, X., Explicit exact solitary wave solutions for the Kundu equation and the derivative Schrödinger equation, Physica Scripta, 64, 1, 7-14 (2001) · Zbl 1064.35184 · doi:10.1238/Physica.Regular.064a00007
[9] Yi, Y.; Liu, Z., The bifurcations of traveling wave solutions of the Kundu equation, Journal of Applied Mathematics, 2013 (2013) · Zbl 1397.35292 · doi:10.1155/2013/137475
[10] Luo, X.; Nadeem, M., Mohand homotopy transform scheme for the numerical solution of fractional Kundu-Eckhaus and coupled fractional massive Thirring equations, Scientific Reports, 13, 1, 3995 (2023) · doi:10.1038/s41598-023-31230-6
[11] Zhang, H., Various exact travelling wave solutions for Kundu equation with fifth-order nonlinear term, Reports on Mathematical Physics, 65, 2, 231-239 (2010) · Zbl 1202.35055 · doi:10.1016/S0034-4877(10)80017-5
[12] Zhang, W.; Qin, Y.; Zhao, Y.; Guo, B., Orbital stability of solitary waves for Kundu equation, Journal of Differential Equations, 247, 5, 1591-1615 (2009) · Zbl 1179.35280 · doi:10.1016/j.jde.2009.05.008
[13] Liu, C.; Liu, J.; Zhou, P.; Chen, M., Exact solutions with bounded periodic amplitude for Kundu equation and derivative nonlinear Schrödinger equation, Journalof Advances in Mathematics and Computer Science, 16, 5, 1-6 (2016) · doi:10.9734/BJMCS/2016/25570
[14] Kundu, A., Exact solutions to higher-order nonlinear equations through gauge transformation, Physica D: Nonlinear Phenomena, 25, 1-3, 399-406 (1987) · Zbl 0612.76002 · doi:10.1016/0167-2789(87)90113-8
[15] Toomanian, M.; Asadi, N., Reductions for Kundu-Eckhaus equation via Lie symmetry analysis, Mathematical Sciences, 7, 1, 50 (2013) · Zbl 1334.37083 · doi:10.1186/2251-7456-7-50
[16] Baskonus, H. M.; Bulut, H., On the complex structures of Kundu-Eckhaus equation via improved Bernoulli sub-equation function method, Waves in Random and Complex Media, 25, 4, 720-728 (2015) · Zbl 1397.35267 · doi:10.1080/17455030.2015.1080392
[17] Wang, P.; Tian, B.; Sun, K.; Qi, F.-H., Bright and dark soliton solutions and Bäcklund transformation for the Eckhaus-Kundu equation with the cubic-quintic nonlinearity, Applied Mathematics and Computation, 251, 233-242 (2015) · Zbl 1328.37055 · doi:10.1016/j.amc.2014.11.014
[18] Ilie, M.; Biazar, J.; Ayati, Z., Resonant solitons to the nonlinear Schrodinger equation with different forms of nonlinearities, Optik, 164, 201-209 (2018) · doi:10.1016/j.ijleo.2018.03.013
[19] Qiu, D.; He, J.; Zhang, Y.; Porsezian, K., The Darboux transformation of the Kundu-Eckhaus equation, Proceedings of the Royal Society A: Mathematical, Physicaland Engineering Sciences, 471, 2180, article 20150236 (2015) · Zbl 1371.35277
[20] Wang, X.; Yang, B.; Chen, Y.; Yang, Y., Higher-order rogue wave solutions of the Kundu-Eckhaus equation, Physica Scripta, 89, 9, article 095210 (2014) · doi:10.1088/0031-8949/89/9/095210
[21] He, J.-H., Homotopy perturbation technique, Computer Methods in Applied Mechanics and Engineering, 178, 3-4, 257-262 (1999) · Zbl 0956.70017 · doi:10.1016/S0045-7825(99)00018-3
[22] Nadeem, M.; Li, F., He-Laplace method for nonlinear vibration systems and nonlinear wave equations, Journal of Low Frequency Noise, Vibration and Active Control, 38, 3-4, 1060-1074 (2019) · doi:10.1177/1461348418818973
[23] Biazar, J.; Ayati, Z.; Yaghouti, M. R., Homotopy perturbation method for homogeneous Smoluchowsk’s equation, Numer. Methods Partial Differential Equation, 26, 5, 1146-1153 (2010) · Zbl 1197.65220 · doi:10.1002/num.20480
[24] Biazar, J.; Ghazvini, H., Exact solutions for nonlinear Burgers’ equation by homotopy perturbation method, Numerical Methods for Partial Differential Equation, 25, 4, 833-842 (2009) · Zbl 1169.65336 · doi:10.1002/num.20376
[25] He, J.-H.; Elagan, S.; Li, Z., Geometrical explanation of the fractional complex transform and derivative chain rule for fractional calculus, Physics Letters, 376, 4, 257-259 (2012) · Zbl 1255.26002 · doi:10.1016/j.physleta.2011.11.030
[26] Li, Z.-B.; He, J.-H., Fractional complex transform for fractional differential equations, Mathematical and Computational Applications, 15, 5, 970-973 (2010) · Zbl 1215.35164 · doi:10.3390/mca15050970
[27] Wang, K.-L.; Yao, S.-W., He’s fractional derivative for the evolution equation, Thermal Science, 24, 4, 2507-2513 (2020) · doi:10.2298/TSCI2004507W
[28] Ain, Q. T.; He, J.-H., On two-scale dimension and its applications, Thermal Science, 23, 3, Part B, 1707-1712 (2019) · doi:10.2298/TSCI190408138A
[29] He, J.-H.; Ji, F.-Y., Two-scale mathematics and fractional calculus for thermodynamics, Thermal Science, 23, 4, 2131-2133 (2019) · doi:10.2298/TSCI1904131H
[30] Arafa, A. A.; Hagag, A. M. S., Q-homotopy analysis transform method applied to fractional Kundu-Eckhaus equation and fractional massive Thirring model arising in quantum field theory, Asian-European Journal of Mathematics, 12, 3, article 1950045 (2019) · Zbl 1419.35198 · doi:10.1142/S1793557119500451
[31] González-Gaxiola, O., The Laplace-Adomian decomposition method applied to the Kundu-Eckhaus equation, International Journal of Mathematics And its Applications, 5, 1(A), 1-12 (2017)
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