First Integral Technique for Finding Exact Solutions of Higher Dimensional Mathematical Physics Models

被引：18

作者：

Javeed, Shumaila ^{[1
]}

Riaz, Sidra ^{[2
]}

Alimgeer, Khurram Saleem ^{[3
]}

Atif, M. ^{[4
]}

Hanif, Atif ^{[5
]}

Baleanu, Dumitru ^{[6
,7
]}

机构：

[1] COMSATS Univ Islambad, Dept Math, Islamabad Campus,Pk Rd, Chak Shahzad Islamabad 45550, Pakistan

[2] Riphah Int Univ, Dept Math, Sect 1-14, Islamabad 45240, Pakistan

[3] COMSATS Univ Islambad, Dept Elect & Comp Engn, Islamabad Campus,Pk Rd, Chak Shahzad Islamabad 45550, Pakistan

[4] King Saud Univ, Coll Sci, Dept Phys & Astron, Riyadh 11451, Saudi Arabia

[5] King Saud Univ, Coll Sci, Bot & Microbiol Dept, Riyadh 11451, Saudi Arabia

[6] Cankaya Univ, Dept Math, Ankara, Turkey

[7] Inst Space Sci, Magurele 06530, Romania

来源：

SYMMETRY-BASEL | 2019年 / 11卷 / 06期

关键词：

first integral method; conformable derivative; modified regularized long wave; potential Kadomtsev Petviashvili equation; coupled dispersive long wave (DLW) system; PARTIAL-DIFFERENTIAL-EQUATIONS; FRACTIONAL BOUSSINESQ;

D O I：

10.3390/sym11060783

中图分类号：

O [数理科学和化学]; P [天文学、地球科学]; Q [生物科学]; N [自然科学总论];

学科分类号：

07 ; 0710 ; 09 ;

摘要：

In this work, we establish the exact solutions of some mathematical physics models. The first integral method (FIM) is extended to find the explicit exact solutions of high-dimensional nonlinear partial differential equations (PDEs). The considered models are: the space-time modified regularized long wave (mRLW) equation, the (1+2) dimensional space-time potential Kadomtsev Petviashvili (pKP) equation and the (1+2) dimensional space-time coupled dispersive long wave (DLW) system. FIM is a powerful mathematical tool that can be used to obtain the exact solutions of many non-linear PDEs.

引用

页数：14

共 28 条

[1] Analytical solution of nonlinear space-time fractional differential equations using the improved fractional Riccati expansion method [J].

Abdel-Salam, Emad A-B. ;

Gumma, Elzain A. E. .

AIN SHAMS ENGINEERING JOURNAL, 2015, 6 (02) :613-620

[2] On conformable fractional calculus [J].

Abdeljawad, Thabet .

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS, 2015, 279 :57-66

[3]

Abu Hammad M., 2014, International Journal of Pure and Applied Mathematics, V94, P215

[4] Nonclassic solitonic structures in DNA's vibrational dynamics [J].

Aguero, Maximo A. ;

De Lourdes Najera, M. A. ;

Carrillo, Mauricio .

INTERNATIONAL JOURNAL OF MODERN PHYSICS B, 2008, 22 (16) :2571-2582

[5] Exponential rational function method for space-time fractional differential equations [J].

Aksoy, Esin ;

Kaplan, Melike ;

Bekir, Ahmet .

WAVES IN RANDOM AND COMPLEX MEDIA, 2016, 26 (02) :142-151

[6] New properties of conformable derivative [J].

Atangana, Abdon ;

Baleanu, Dumitru ;

Alsaedi, Ahmed .

OPEN MATHEMATICS, 2015, 13 :889-898

[7] A conformable fractional calculus on arbitrary time scales [J].

Benkhettou, Nadia ;

Hassani, Salima ;

Torres, Delfim F. M. .

JOURNAL OF KING SAUD UNIVERSITY SCIENCE, 2016, 28 (01) :93-98

[8] The solitary wave solution of the two-dimensional regularized long-wave equation in fluids and plasmas [J].

Dehghan, Mehdi ;

Salehi, Rezvan .

COMPUTER PHYSICS COMMUNICATIONS, 2011, 182 (12) :2540-2549

[9] 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

[10] New exact travelling wave solutions using modified extended tanh-function method [J].

El-Wakil, S. A. ;

Abdou, M. A. .

CHAOS SOLITONS & FRACTALS, 2007, 31 (04) :840-852

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