A (2+1)-dimensional generalized Hirota-Satsuma-Ito equations: Lie symmetry analysis, invariant solutions and dynamics of soliton solutions

被引:55
作者
Kumar, Sachin [1 ]
Nisar, Kottakkaran Sooppy [2 ]
Kumar, Amit [3 ]
机构
[1] Univ Delhi, Fac Math Sci, Dept Math, Delhi 110007, India
[2] Prince Sattam bin Abdulaziz Univ, Coll Arts & Sci, Dept Math, Wadi Aldawaser 11991, Saudi Arabia
[3] Univ Delhi, Sri Vankateswara Coll, Dept Math, Delhi 110021, India
关键词
Lie symmetry technique; Infinitesimal generators; Generalized HSI equations; Exact solutions; Solitons; CONSERVATION-LAWS; SYSTEM;
D O I
10.1016/j.rinp.2021.104621
中图分类号
T [工业技术];
学科分类号
08 ;
摘要
This paper investigates the exact invariant solutions and the dynamics of soliton solutions to the (2+1)-dimensional generalized Hirota-Satsuma-Ito (g-HSI) equations. By applying the Lie symmetry technique, infinitesimal vectors, the commutation relations, and various similarity reductions are derived from the gHSI equations. Using the two stages of Lie symmetry reductions, the equation is transformed into various nonlinear ordinary differential equations (NLODEs). After that, by solving the various resulting ODEs, we obtain abundant explicit exact solutions in terms of the involved functional parameters. These closed-form invariant solutions are successfully presented in the form of distinct complex wave-structures of solutions like comboform solitons, dark-bright solitons, W-shaped solitons, the interaction between multiple solitons, parabolic wave solitons, multi-wave structures, and curved-shaped parabolic solitons. Furthermore, using computerized symbolic computation and numerical simulation, the physical behaviors of some obtained solutions are displayed in three-dimensional graphics. The resulting solutions are found to be useful for understanding the dynamics of the exact closed-form solutions of this model and show the authenticity as well as the effectiveness of the proposed method. Therefore, the gained solutions and their dynamical wave structures are quite significant for understanding the propagation of the excitation waves in shallow water wave models. Furthermore, using the resulting symmetries, the conservation laws of g-HSI equations have been obtained by applying Ibragimov's theorem.
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页数:13
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共 54 条
[1]   Comprehensive analysis of the symmetries and conservation laws of the geodesic equations for a particular string inspired FRLW solution [J].
Ahangari, Fatemeh .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2017, 42 :645-674
[2]   Direct construction of conservation laws from field equations [J].
Anco, SC ;
Bluman, G .
PHYSICAL REVIEW LETTERS, 1997, 78 (15) :2869-2873
[3]  
[Anonymous], 2020, INT J MOD PHYS B, V34
[4]  
Bluman G. W., 2013, Symmetries and Differential Equations, V81
[5]   Solving Nonlinear Fractional Partial Differential Equations Using the Homotopy Analysis Method [J].
Dehghan, Mehdi ;
Manafian, Jalil ;
Saadatmandi, Abbas .
NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2010, 26 (02) :448-479
[6]   METHOD FOR SOLVING KORTEWEG-DEVRIES EQUATION [J].
GARDNER, CS ;
GREENE, JM ;
KRUSKAL, MD ;
MIURA, RM .
PHYSICAL REVIEW LETTERS, 1967, 19 (19) :1095-&
[7]   The Lie symmetry analysis and exact Jacobi elliptic solutions for the Kawahara-KdV type equations [J].
Ghanbari, Behzad ;
Kumar, Sachin ;
Niwas, Monika ;
Baleanu, Dumitru .
RESULTS IN PHYSICS, 2021, 23
[8]   On exploring optical solutions to the Hirota equation through an efficient analytical method [J].
Gunay, B. .
RESULTS IN PHYSICS, 2021, 27
[9]   SOME NONCONFORMAL ACCELERATING PERFECT FLUID PLATES OF EMBEDDING CLASS 1 USING SIMILARITY TRANSFORMATIONS [J].
Gupta, Y. K. ;
Pratibha ;
Kumar, Sachin .
INTERNATIONAL JOURNAL OF MODERN PHYSICS A, 2010, 25 (09) :1863-1879
[10]   Nonlinear self-adjointness and conservation laws [J].
Ibragimov, N. H. .
JOURNAL OF PHYSICS A-MATHEMATICAL AND THEORETICAL, 2011, 44 (43)