Soliton solutions, Painleve analysis and conservation laws for a nonlinear evolution equation

被引：57

作者：

Rizvi, S. T. R. ^{[1
]}

Seadawy, Aly R. ^{[2
]}

Younis, Muhammad ^{[3
]}

Ali, Ijaz ^{[1
]}

Althobaiti, S. ^{[4
]}

Mahmoud, Samy F. ^{[5
]}

机构：

[1] COMSATS Univ Islamabad, Dept Math, Lahore Campus, Lahore, Pakistan

[2] Taibah Univ, Fac Sci, Math Dept, Al Madinah Al Munawarah, Saudi Arabia

[3] Univ Punjab, PUCIT, Lahore, Pakistan

[4] Taif Univ, Ranyah Univ Coll, Technol & Sci Dept, POB 11099, At Taif 21944, Saudi Arabia

[5] Taif Univ, Coll Sci, Dept Biotechnol, POB 11099, At Taif 21944, Saudi Arabia

来源：

RESULTS IN PHYSICS | 2021年 / 23卷

关键词：

Unified method; Conservation laws; Nonlinear equation; P test; TRAVELING-WAVE SOLUTIONS; DIFFERENTIAL-EQUATIONS; DYNAMICAL EQUATION; BEAM;

D O I：

10.1016/j.rinp.2021.103999

中图分类号：

T [工业技术];

学科分类号：

08 ;

摘要：

In this paper, we investigate a reputed nonlinear partial differential equation (NLPDE) known as geophysical Korteweg-de Vries (GPKdV) equation. We implement a renowned Unified method (UM) of nonlinear (NL) sciences for the extraction of polynomial and rational function solutions of GPKdV equation, which degenarate to various wave solutions like solitary, soliton (dromions) and elliptic wave solutions. Further more, for the analysis of the integrability of our governing model, we apply Painleve? (P) algorithm to check the singularities structure of the model. The fulfillment of all the requirements of the P test indicates the solvability of the governing equation with the help of inverse scattering transformation (IST) or some linear techniques. Moreover, we calculate conservation laws (CLs) in polynomial form as conserved fluxes and densities by implementing dilation symmetry. We utilize Euler and Homotopy operators for the evaluation of the intended conserved quantities.

引用

页数：7

共 41 条

[1] Towards a Unified Method for Exact Solutions of Evolution Equations. An Application to Reaction Diffusion Equations with Finite Memory Transport [J].

Abdel-Gawad, H. I. .

JOURNAL OF STATISTICAL PHYSICS, 2012, 147 (03) :506-518

[2]

Abdou M.A., 2011, INT J NONLINEAR SCI, V12, P131

[3]

Ablowitz M J., 1991, SOLITON NONLINEAR EV

[4] A CONNECTION BETWEEN NON-LINEAR EVOLUTION-EQUATIONS AND ORDINARY DIFFERENTIAL-EQUATIONS OF P-TYPE .1. [J].

ABLOWITZ, MJ ;

RAMANI, A ;

SEGUR, H .

JOURNAL OF MATHEMATICAL PHYSICS, 1980, 21 (04) :715-721

[5]

Adams P., 2003, THESIS

[6] Investigation of Coriolis effect on oceanic flows and its bifurcation via geophysical Korteweg-de Vries equation [J].

Ak, Turgut ;

Saha, Asit ;

Dhawan, Sharanjeet ;

Kara, Abdul Hamid .

NUMERICAL METHODS FOR PARTIAL DIFFERENTIAL EQUATIONS, 2020, 36 (06) :1234-1253

[7] Computational methods and traveling wave solutions for the fourth-order nonlinear Ablowitz-Kaup-Newell-Segur water wave dynamical equation via two methods and its applications [J].

Ali, Asghar ;

Seadawy, Aly R. ;

Lu, Dianchen .

OPEN PHYSICS, 2018, 16 (01) :219-226

[8] Conserved quantities along with Painleve analysis and optical solitons for the nonlinear dynamics of Heisenberg ferromagnetic spin chains model [J].

Ali, I. ;

Seadawy, A. R. ;

Rizvi, S. T. R. ;

Younis, M. ;

Ali, K. .

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2020, 34 (30)

[9] Elliptic function and solitary wave solutions of the higher-order nonlinear Schrodinger dynamical equation with fourth-order dispersion and cubic-quintic nonlinearity and its stability [J].

Arshad, M. ;

Seadawy, Aly R. ;

Lu, Dianchen .

EUROPEAN PHYSICAL JOURNAL PLUS, 2017, 132 (08)

[10]

Baldwin DE, 2004, THESIS

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