New Periodic and Localized Traveling Wave Solutions to a Kawahara-Type Equation: Applications to Plasma Physics

被引：31
作者：
Alyousef, Haifa A. [1 ]
Salas, Alvaro H. [2 ]
Alharthi, M. R. [3 ]
El-Tantawy, S. A. [4 ,5 ]
机构：
[1] Princess Nourah bint Abdulrahman Univ, Coll Sci, Dept Phys, POB 84428, Riyadh 11671, Saudi Arabia
[2] Univ Nacl Colombia, FIZMAKO Res Grp, Dept Math & Stat, Sede Manizales, Colombia
[3] Taif Univ, Coll Sci, Dept Math & Stat, POB 11099, Taif 21944, Saudi Arabia
[4] Port Said Univ, Fac Sci, Dept Phys, Port Said 42521, Egypt
[5] Al Baha Univ, Fac Sci & Arts, Dept Phys, Res Ctr Phys RCP, Al Bahah, Saudi Arabia
来源：
COMPLEXITY | 2022年 / 2022卷
关键词：
SOLITARY WAVES; COLLISION;
D O I：
10.1155/2022/9942267
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this study, some new hypotheses and techniques are presented to obtain some new analytical solutions (localized and periodic solutions) to the generalized Kawahara equation (gKE). As a particular case, some traveling wave solutions to both Kawahara equation (KE) and modified Kawahara equation (mKE) are derived in detail. Periodic and soliton solutions to this family are obtained. The periodic solutions are expressed in terms of Weierstrass elliptic functions (WSEFs) and Jacobian elliptic functions (JEFs). For KE, some direct and indirect approaches are carried out to derive the periodic and localized solutions. For mKE, two different hypotheses in the form of WSEFs are used to derive the periodic and localized solutions. Also, the cnoidal wave solutions in the form of JEFs are obtained. As a realistic physical application, the solutions obtained can be dedicated to studying many nonlinear waves that propagate in plasma.
引用
收藏
页数：15
相关论文
共 35 条
[1]   Novel anlytical solution to the damped Kawahara equation and its application for modeling the dissipative nonlinear structures in a fluid medium [J].
Aljahdaly, Noufe H. ;
El-Tantawy, S. A. .
JOURNAL OF OCEAN ENGINEERING AND SCIENCE, 2022, 7 (05) :492-497
[2]  
Allahverdiyeva N., 2021, ADV MATH MOD APPL, V6, P128
[3]   Solitary wave solution for the generalized Kawahara equation [J].
Biswas, Anjan .
APPLIED MATHEMATICS LETTERS, 2009, 22 (02) :208-210
[4]   Backlund transformation, exact solutions and interaction behaviour of the (3+1)-dimensional Hirota-Satsuma-Ito-like equation [J].
Chen, Si-Jia ;
Ma, Wen-Xiu ;
Lu, Xing .
COMMUNICATIONS IN NONLINEAR SCIENCE AND NUMERICAL SIMULATION, 2020, 83
[5]   On the dissipative extended Kawahara solitons and cnoidal waves in a collisional plasma: Novel analytical and numerical solutions [J].
El-Tantawy, S. A. ;
Salas, Alvaro H. ;
Alharthi, M. R. .
PHYSICS OF FLUIDS, 2021, 33 (10)
[6]   Novel analytical cnoidal and solitary wave solutions of the Extended Kawahara equation [J].
El-Tantawy, S. A. ;
Salas, Alvaro H. ;
Alharthi, M. R. .
CHAOS SOLITONS & FRACTALS, 2021, 147
[7]   A new approach for modelling the damped Helmholtz oscillator: applications to plasma physics and electronic circuits [J].
El-Tantawy, S. A. ;
Salas, Alvaro H. ;
Alharthi, M. R. .
COMMUNICATIONS IN THEORETICAL PHYSICS, 2021, 73 (03)
[8]   Nonlinear dynamics of soliton collisions in electronegative plasmas: The phase shifts of the planar KdV- and mkdV-soliton collisions [J].
El-Tantawy, S. A. .
CHAOS SOLITONS & FRACTALS, 2016, 93 :162-168
[9]   Head-on collision of ion-acoustic solitons in an ultracold neutral plasma [J].
El-Tantawy, S. A. ;
Moslem, W. M. ;
Sabry, R. ;
El-Labany, S. K. ;
El-Metwally, M. ;
Schlickeiser, R. .
ASTROPHYSICS AND SPACE SCIENCE, 2014, 350 (01) :175-184
[10]   Super rogue waves in ultracold neutral nonextensive plasmas [J].
El-Tantawy, S. A. ;
El-Bedwehy, N. A. ;
Moslem, W. M. .
JOURNAL OF PLASMA PHYSICS, 2013, 79 :1049-1056
1234