YE Feiyun,LIU Xiaohua,ZENG Zhiyun.Traveling wave solutions of generalized third - order nonlinear Schrdinger equations[J].Journal of Yanbian University,2022,(04):312-317.
广义三阶非线性薛定谔方程的行波解
- Title:
- Traveling wave solutions of generalized third - order nonlinear Schrödinger equations
- 文章编号:
- 1004-4353(2022)04-0312-06
- 关键词:
- 广义三阶非线性薛定谔方程; 双曲正切函数展开法; 行波解
- Keywords:
- generalized third - order nonlinear Schrö; dinger equation; hyperbolic tanh - function expansion method; traveling wave solutions
- 分类号:
- O175.29
- 文献标志码:
- A
- 摘要:
- 利用改进的双曲正切函数展开法研究了广义三阶非线性薛定谔方程的行波解,得到了其双曲函数解、有理函数解和三角函数解的精确表达式,其中两组双曲函数解的精确表达式是新解.利用Maple软件给出了解在具体参数值下的3D图和2D图,并通过分析解的性态得出了相应解的类型.
- Abstract:
- In this paper, the traveling wave solutions of the generalized third - order nonlinear Schrödinger equation are studied by using the hyperbolic tanh - function expansion method, and the exact expressions of hyperbolic, rational and trigonometric function solutions are obtained.The exact expressions of the solutions of two sets of hyperbolic functions are new solutions.The 3D and 2D graphs under specific parameter values are given by Maple software, and the types of corresponding solutions are obtained by analyzing the properties of the solutions.
参考文献/References:
[1] BENJAMIN T B, FEIR J E.The disintegration of wave trains on deep water: Part 1: Theory[J].Journal of Fluid Mechanics, 1967,27(3):417 - 430.
[2] RAZA N, ARSHED S, JAVID A.Optical solitons and stability analysis for the generalized second - order nonlinear Schrödinger equation in an optical fiber[J].International Journal of Nonlinear Sciences and Numerical Simulation, 2020,21(7/8):855 - 863.
[3] ZHOU Y B, WANG M L, WANG Y M.Periodic wave solutions to a coupled KdV equations with variable coefficients[J].Physics Letters A, 2003,308(1):31 - 36.
[4] ZHOU Q, EKICI M, MIRZAZADEH M, et al.The investigation of soliton solutions of the coupled Sine - Gordon equation in nonlinear optics[J].Journal of Modern Optics, 2017,64(16):1677 - 1682.
[5] ZAYED E M E, ALURRFI K A E.Extended auxiliary equation method and its applications for finding the exact solutions for a class of nonlinear Schrödinger - type equations[J].Applied Mathematics and Computation, 2016,289:120 - 130.
[6] BAHRAMI B S, ABDOLLAHZADEH H, BERIJANI I M, et al.Exact travelling solutions for some nonlinear physical models by(G'/G)- expansion method[J].Pramana, 2011,77(2):263 - 275.
[7] ZHANG Y P, DAI C Q.Some remarks on the Riccati equation expansion method for variable separation of nonlinear models[J].Zeitschrift für Naturforschung A, 2015,70(10):835 - 842.
[8] TRIKI H, AK T, EKICI M, et al.Some new exact wave solutions and conservation laws of potential Korteweg - de Vries equation[J].Nonlinear Dynamics, 2017,89(1):501 - 508.
[9] LU D, SEADAWY A R, WANG J, et al.Soliton solutions of the generalised third - order nonlinear Schrödinger equation by two mathematical methods and their stability[J].Pramana, 2019,93(3):1 - 9.
[10] HOSSEINI K, OSMAN M S, MIRZAZADEH M, et al.Investigation of different wave structures to the generalized third - order nonlinear Scrödinger equation[J].Optik, 2020,206:164259.
[11] NASREEN N, SEADAWY A R, LU D, et al.Dispersive solitary wave and soliton solutions of the gernalized third order nonlinear Schrödinger dynamical equation by modified analytical method[J].Results in Physics, 2019,15:102641.
[12] RABIE W B, SEADAWY A R, AHMED H M.Highly dispersive optical solitons to the generalized third - order nonlinear Schrödinger dynamical equation with applications[J].Optik, 2021,241:167109.
[13] AL - KALBANI K K, AL - GHAFRI K S, KRISHNAN E V, et al.Pure - cubic optical solitons by Jacobi's elliptic function approach[J].Optik, 2021,243:167404.
[14] MALIK S, KUMAR S, NISAR K S, et al.Different analytical approaches for finding novel optical solitons with generalized third - order nonlinear Schrödinger equation[J].Results in Physics, 2021,29:104755.
[15] LIU S, REZAEI S, NAJATI S A, et al.Novel wave solutions to a generalized third - order nonlinear Schrödinger's equation[J].Results in Physics, 2022,37:105457.
[16] ALAM L M B, JIANG X.Exact and explicit traveling wave solution to the time - fractional phi - four and(2+1)dimensional CBS equations using the modified extended tanh - function method in mathematical physics[J].Partial Differential Equations in Applied Mathematics, 2021,4:100039.
备注/Memo
收稿日期: 2022-09-15
基金项目: 贵州省教育厅自然科学研究项目(黔教技[2022]015号)
第一作者: 叶飞筠(1998—),女,硕士研究生,研究方向为微分方程定性分析及孤波解.
通信作者: 刘小华(1975—),女,博士,教授,研究方向为微分方程定性分析及孤波解.