[1]
|
G. W. Bluman and S. Kumei, Symmetries and Differential Equations, Springer-Verlag, New York, 1989.
Google Scholar
|
[2]
|
G. W. Bluman, A. F. Cheviakov and S.C. Anco, Applications of Symmetry Methods to Partial Differential Equations, Springer, New York, 2010.
Google Scholar
|
[3]
|
G. W. Bluman and A. F. Cheviakov, Framework for potential systems and nonlocal symmetries: Algorithmic approach, J. Math. Phys., 2005, 46, 123506. doi: 10.1063/1.2142834
CrossRef Google Scholar
|
[4]
|
C. Chun and B. Neta, Comparative study of methods of various orders for finding simple roots of nonlinear equations, J. Appl. Anal. Comput., 2019, 9(2), 400-427.
Google Scholar
|
[5]
|
S. Chen, B. Tian, Y. Sun and C. Zhang, Generalized Darboux Transformations, Rogue Waves, and Modulation Instability for the Coherently Coupled Nonlinear Schrödinger Equations in Nonlinear Optics, Ann. Phys. (Berlin), 2019, 531(8), 1900011. doi: 10.1002/andp.201900011
CrossRef Google Scholar
|
[6]
|
Z. Cheng and Z. Bi, Study on a kind of p-Laplacian neutral differential equation with multiple variable coefficients, J. Appl. Anal. Comput., 2019, 9(2), 501-525.
Google Scholar
|
[7]
|
X. Du, B. Tian, Q. Qu, Y. Yuan and X. Zhao, Lie group analysis, solitons, self-adjointness and conservation laws of the modified Zakharov-Kuznetsov equation in an electron-positron-ion magnetoplasma, Chaos Solitons Fract., 2020, 134, 109709. doi: 10.1016/j.chaos.2020.109709
CrossRef Google Scholar
|
[8]
|
Z. Du, B. Tian, H. Chai and X. Zhao, Dark-bright semi-rational solitons and breathers for a higher-order coupled nonlinear Schrödinger system in an optical fiber, Appl. Math. Lett., 2020, 102, 106110. doi: 10.1016/j.aml.2019.106110
CrossRef Google Scholar
|
[9]
|
A. Deliceoglu and D. Bozkurt, Structural bifurcation of divergence-free vector fields near non-simple degenerate points with symmetry, J. Appl. Anal. Comput., 2019, 9(2), 718-738.
Google Scholar
|
[10]
|
F. Galas, New nonlocal symmetries with pseudopotentials, J. Phys. A: Math. Gen., 1992, 25, L981. doi: 10.1088/0305-4470/25/15/014
CrossRef Google Scholar
|
[11]
|
X. Gao, Mathematical view with observational/experimental consideration on certain (2+1)-dimensional waves in the cosmic/laboratory dusty plasmas, Appl. Math. Lett., 2019, 91, 165-172. doi: 10.1016/j.aml.2018.11.020
CrossRef Google Scholar
|
[12]
|
X. Gao, Y. Guo and W. Shan, Water-wave symbolic computation for the Earth, Enceladus and Titan: The higher-order Boussinesq-Burgers system, auto- and non-auto-Bäcklund transformations, Appl. Math. Lett., 2020, 104, 106170. doi: 10.1016/j.aml.2019.106170
CrossRef Google Scholar
|
[13]
|
C. Hu, B. Tian, H. Yin, C. Zhang and Z. Zhang, Dark breather waves, dark lump waves and lump wave-soliton interactions for a (3+1)-dimensional generalized Kadomtsev-Petviashvili equation in a fluid, Comput. Math. Appl., 2019, 78, 166-177. doi: 10.1016/j.camwa.2019.02.026
CrossRef Google Scholar
|
[14]
|
X. Hu, S. Lou and Y. Chen, Explicit solutions from eigenfunction symmetry of the Korteweg-de Vries equation, Phys. Rev. E, 2012, 85, 85056607-1.
Google Scholar
|
[15]
|
J. Han and L. Yan, A time fractional functional differential equation driven by the fractional Brownian motion, J. Appl. Anal. Comput., 2019, 9(2), 547-567.
Google Scholar
|
[16]
|
Q. Huang, Y. Gao, and Y. Feng, Lax pair, infinitely-many conservation laws and soliton solutions for a set of the time-dependent Whitham-Broer-Kaup equations for the shallow water, Waves in Random and Complex Media 2019, 29(1), 19-33.
Google Scholar
|
[17]
|
N. H. Ibragimov, Transformation Groups Applied to Mathematical Physics, Boston, MA: Reidel, 1985.
Google Scholar
|
[18]
|
H. Khan, C. Tunc and A. Khan, Stability results and existence theorems for nonlinear delay-fractional differential equations with $\phi{^*_p}$-operator, J. Appl. Anal. Comput., 2020, 10(2), 584-597.
Google Scholar
|
[19]
|
B. Zeng, J. Yang and B. Ren, Exact solutions and residual symmetries of the Ablowitz-Kaup-Newell-Segur system, Chin. Phys. B, 2015, 24(1), 010202. doi: 10.1088/1674-1056/24/1/010202
CrossRef Google Scholar
|
[20]
|
S. Lie, über die Integration durch bestimmte Integrale von einer Classe linearer partieller Differentialgleichungen, Arch. Math. 1881, 6, 328-368.
Google Scholar
|
[21]
|
S. Lou, X. Hu and Y. Chen, Nonlocal symmetries related to Bäcklund transformation and their applications, J. Phys. A: Math. Theor., 2012, 45, 155209. doi: 10.1088/1751-8113/45/15/155209
CrossRef Google Scholar
|
[22]
|
Q. Miao, X. Xin and Y. Chen, Nonlocal symmetries and explicit solutions of the AKNS system, Appl. Math. Lett., 2014, 28, 7-13. doi: 10.1016/j.aml.2013.09.002
CrossRef Google Scholar
|
[23]
|
P. J. Olver, Applications of Lie Groups to Differential Equations, Berlin: Springer, 1986.
Google Scholar
|
[24]
|
L. V. Ovsiannikov, Group Analysis of Differential Equations, New York: Academic, 1982.
Google Scholar
|
[25]
|
C. Qin, S. Tian, L. Zou, et al, Lie symmetry analysis, conservation laws and exact solutions of fourth-order time fractional Burgers equation, J. Appl. Anal. Comput., 2018, 8(6), 1727-1746.
Google Scholar
|
[26]
|
W. Qian, Y. Li and X. Yang, The Isoenergetic KAM-Type Theorem at Resonant Case for Nearly Integrable Hamiltonian Systems, J. Appl. Anal. Comput., 2019, 9(5), 1616-1638.
Google Scholar
|
[27]
|
S. Sui and B. Li, Bifurcation of limit cycles from the global center of a class of integrable non-Hamilton systems, J. Appl. Anal. Comput., 2018, 8(5), 1441-1451.
Google Scholar
|
[28]
|
M. Wang, B. Tian, Y. Sun and Z. Zhang, Lump, mixed lump-stripe and rogue wave-stripe solutions of a (3+1)-dimensional nonlinear wave equation for a liquid with gas bubbles, Comput. Math. Appl., 2020, 79, 576-587. doi: 10.1016/j.camwa.2019.07.006
CrossRef Google Scholar
|
[29]
|
X. Xin and X. Liu, Interaction Solutions for (1+1)-Dimensional Higher-Order Broer-Kaup System, Commun. Theor. Phys., 2016, 66(5), 479-482. doi: 10.1088/0253-6102/66/5/479
CrossRef Google Scholar
|
[30]
|
X. Xin, Y. Liu and X. Liu, Nonlocal symmetries, exact solutions and conservation laws of the coupled Hirota equations, Appl. Math. Lett., 2016, 55, 63-71. doi: 10.1016/j.aml.2015.11.009
CrossRef Google Scholar
|
[31]
|
Y. Xia, X. Xin and S. Zhang, Residual symmetry, interaction solutions, and conservation laws of the (2+1)-dimensional dispersive long-wave system, Chin. Phys. B, 2017, 26(3), 030202. doi: 10.1088/1674-1056/26/3/030202
CrossRef Google Scholar
|
[32]
|
X. Xin, L. Zhang, Y. Xia, et al. Nonlocal symmetries and exact solutions of the (2+1)-dimensional generalized variable coefficient shallow water wave equation, Appl. Math. Lett., 2019, 94, 112-119. doi: 10.1016/j.aml.2019.02.028
CrossRef Google Scholar
|
[33]
|
X. Xin, H. Liu, L. Zhang, et al. High order nonlocal symmetries and exact interaction solutions of the variable coefficient KdV equation, Appl. Math. Lett., 2019, 88, 132-140. doi: 10.1016/j.aml.2018.08.023
CrossRef Google Scholar
|
[34]
|
H. Yin, B. Tian and X. Zhao, Chaotic breathers and breather fission/fusion for a vector nonlinear Schrödinger equation in a birefringent optical fiber or wavelength division multiplexed system, Appl. Math. Comput., 2020, 368, 124768.
Google Scholar
|
[35]
|
X. Zheng and L. Wei, Symmetry analysis conservation laws of a time fractional fifth-order Sawada-Kotera equation, J. Appl. Anal. Comput., 2017, 7(4), 1275-1284.
Google Scholar
|
[36]
|
Z. Zhao and B. Han, On Symmetry Analysis and Conservation Laws of the AKNS System, Z. Naturforsch., 2016, 71(8)a, 741-750.
Google Scholar
|
[37]
|
C. Zhang, B. Tian, Q. Qu, L. Liu and H. Tian, Vector bright solitons and their interactions of the couple Fokas-Lenells system in a birefringent optical fiber, Z. Angew. Math. Phys., 2020, 71(1), 1-19.
Google Scholar
|