Nonlinear self-adjointness, conserved quantities, bifurcation analysis and travelling wave solutions of a family of long-wave unstable lubrication model

被引:44
作者
Jhangeer, Adil [1 ]
Raza, Nauman [2 ]
Rezazadeh, Hadi [3 ]
Seadawy, Aly [4 ,5 ]
机构
[1] Namal Inst, Dept Math, 30 KM Talagang Rd, Mianwali 42250, Pakistan
[2] Univ Punjab, Dept Math, Lahore, Pakistan
[3] Amol Univ Special Modern Technol, Fac Engn Technol, Amol, Iran
[4] Taibah Univ, Fac Sci, Math Dept, Al Madinah Al Munawarah, Saudi Arabia
[5] Beni Suef Univ, Fac Sci, Math Dept, Bani Suwayf, Egypt
来源
PRAMANA-JOURNAL OF PHYSICS | 2020年 / 94卷 / 01期
关键词
Nonlinear self-adjointness; bifurcation analysis; analytic solutions; long-wave unstable lubrication model; 02; 20; Sv; 30; Jr; 11; -i; 47; Ky; KUNDU-LAKSHMANAN EQUATION; OPTICAL SOLITONS; EXPANSION METHOD; EVOLUTION; SUBCLASSES; LAWS;
D O I
10.1007/s12043-020-01961-6
中图分类号
O4 [物理学];
学科分类号
0702 ;
摘要
The paper investigates a class of long-wave unstable lubrication model using Lie theory. A nonlinear self-adjoint classification of the considered equation is carried out. Without having to go into microscopic details of the physical aspects, non-trivial conservation laws are computed. Then, minimal set of Lie point symmetries of the discussed model is classified up to one-dimensional conjugacy classes which are further utilised one by one to construct the similarity variables to reduce the dimension of the considered model. After that, all possible phase trajectories are classified with respect to the parameters of the equation. Some travelling wave and kink-wave solutions are also showed and graphical representations are displayed to depict their propagation.
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页数:9
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共 40 条
  • [1] Ablowitz MJ, 1991, Nonlinear Evolution Equations and Inverse Scattering
  • [2] Performance of a hybrid computational scheme on traveling waves and its dynamic transition for Gilson-Pickering equation
    Ak, Turgut
    Saha, Asit
    Dhawan, Sharanjeet
    [J]. INTERNATIONAL JOURNAL OF MODERN PHYSICS C, 2019, 30 (04):
  • [3] Traveling wave and exact solutions for the perturbed nonlinear Schrodinger equation with Kerr law nonlinearity
    Akram, Ghazala
    Mahak, Nadia
    [J]. EUROPEAN PHYSICAL JOURNAL PLUS, 2018, 133 (06):
  • [4] Exact solutions, conservation laws, bifurcation of nonlinear and supernonlinear traveling waves for Sharma-Tasso-Olver equation
    Ali, Muhammad Nasir
    Husnine, Syed Muhammad
    Saha, Asit
    Bhowmik, Samir Kumar
    Dhawan, Sharanjeet
    Ak, Turgut
    [J]. NONLINEAR DYNAMICS, 2018, 94 (03) : 1791 - 1801
  • [5] Direct construction method for conservation laws of partial differential equations - Part II: General treatment
    Anco, SC
    Bluman, G
    [J]. EUROPEAN JOURNAL OF APPLIED MATHEMATICS, 2002, 13 : 567 - 585
  • [6] Bertozzi AL, 1998, COMMUN PUR APPL MATH, V51, P625, DOI 10.1002/(SICI)1097-0312(199806)51:6<625::AID-CPA3>3.0.CO
  • [7] 2-9
  • [8] Bertozzi AL, 2000, INDIANA U MATH J, V49, P1323
  • [9] Bessel-Hagen E., 1921, Math. Annalen, V84, P258
  • [10] Highly dispersive optical solitons with quadratic-cubic law by exp-function
    Biswas, Anjan
    Ekici, Mehmet
    Sonmezoglu, Abdullah
    Belic, Milivoj R.
    [J]. OPTIK, 2019, 186 (431-435): : 431 - 435