Explicit Soliton Structure Formation for the Riemann Wave Equation and a Sensitive Demonstration

被引:66
作者
Majid, Sheikh Zain [1 ]
Faridi, Waqas Ali [1 ]
Asjad, Muhammad Imran [1 ]
Abd El-Rahman, Magda [2 ,3 ]
Eldin, Sayed M. [4 ]
机构
[1] Univ Management & Technol, Dept Math, Lahore 54782, Pakistan
[2] King Khalid Univ, Coll Sci, Dept Phys, Abha 61413, Saudi Arabia
[3] Natl Ctr Radiat Res & Technol NCRRT, Dept Radiat Phys, Atom Energy Author, Cairo 11787, Egypt
[4] Future Univ Egypt, Fac Engn, Ctr Res, New Cairo 11835, Egypt
关键词
new extended direct algebraic methodology; Riemann wave equation; soliton solutions; sensitivity analysis; SYSTEM;
D O I
10.3390/fractalfract7020102
中图分类号
O1 [数学];
学科分类号
0701 ; 070101 ;
摘要
The motive of the study was to explore the nonlinear Riemann wave equation, which describes the tsunami and tidal waves in the sea and homogeneous and stationary media. This study establishes the framework for the analytical solutions to the Riemann wave equation using the new extended direct algebraic method. As a result, the soliton patterns of the Riemann wave equation have been successfully illustrated, with exact solutions offered by the plane solution, trigonometry solution, mixed hyperbolic solution, mixed periodic and periodic solutions, shock solution, mixed singular solution, mixed trigonometric solution, mixed shock single solution, complex soliton shock solution, singular solution, and shock wave solutions. Graphical visualization is provided of the results with suitable values of the involved parameters by Mathematica. It was visualized that the velocity of the soliton and the wave number controls the behavior of the soliton. We are confident that our research will assist physicists in predicting new notions in mathematical physics.
引用
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页数:23
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