Explicit exact solutions for (2+1)-dimensional Boiti–Leon–Pempinelli equation

Feng, Wei-Gui; Li, Kaiming; Li, Ya-Zhou; Chang, Lin

doi:10.1016/j.cnsns.2008.06.005

Cited by 21 publications

(21 citation statements)

References 20 publications

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“…Yurov [44] [20] to search for exact and explicit solutions. Recently, a new mapping method is used by Dai and Wang [11] to obtain the variable separation solutions (with two arbitrary functions) of the BLP equation, and so forth.…”

Section: İ Aslanmentioning

confidence: 99%

Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation

Aslan

2011

International Journal of Computer Mathematics

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This paper deals with the so-called Exp-function method for studying a particular nonlinear partial differential equation (PDE): the (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. The method is constructive and can be carried out in a computer with the aid of a computer algebra system. The obtained generalized solitary wave solutions contain more arbitrary parameters compared with the earlier works, and thus, they are wider. This means that our method is effective and powerful for constructing exact and explicit analytic solutions to nonlinear PDEs.

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Section: İ Aslanmentioning

confidence: 99%

Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation

Aslan

2011

International Journal of Computer Mathematics

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“…By taking h 1 = h 0 = 0, and using [21], we have the triangular and solitary wave solutions as follows…”

Section: Familymentioning

confidence: 99%

A series of new exact solutions of nonlinear evolution equations

Abdou

2010

Numerical Methods Partial

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With the aid of computer symbolic computation system Maple, the generalized auxiliary equation method is first applied to two nonlinear evolution equations, namely, the nonlinear elastic rod equation and (2 + 1)-dimensional Boiti-Leon-Pempinelli equation. As a results, some new types of exact traveling wave solutions are obtained which include bell and kink profile solitary wave solutions, and triangular periodic wave solutions and singular solutions. The method is straightforward and concise, and it can also be applied to other nonlinear evolution equations in mathematical physics.

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“…The BLP system has extensive physical background [8][9][10][11][12][13][14][15][16][17][18]. Boiti et al [5] established the integrability of the system by using sine-Gordon and sinh-Gordon equations.…”

Section: Introductionmentioning

confidence: 99%

“…The BLP system and other NLEEs are solved by many efficient methods, notably object reduction approach [8], extended tanh method [9], homotopy analysis and homotopy Padé methods [10], Bifurcation method [11], new mapping method [12], improved projective Riccati equation method [13], Special Painlevé Bäcklund transformations and multilinear variable separation approach [15], modified Clarkson and Kruskal (CK) direct method [16], generalized algebra method [17], tanh-coth method [18], sinh-cosh and sin-cos methods [19] and tan-cot method [20], etc.…”

Section: Introductionmentioning

confidence: 99%

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Some more similarity solutions of the(2+1)-dimensional BLP system

Kumar

2015

Computers & Mathematics with Applications

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2 + 1)-dimensional Boiti-Leon-Pempinelli system Exact solutions Similarity transformations method a b s t r a c t Some more similarity solutions of the coupled Boiti-Leon-Pempinelli system have been obtained by using similarity transformations method via Lie-group theory. The solutions are attained under the restrictions imposed on the functions involved in infinitesimals. Then, solutions are investigated through the graphical representation in different cases. The cases depend upon some suitable choice of arbitrary functions involved there i.e. in the solutions to get physically meaningful structures. Analytical solutions are supplemented by numerical simulations with appropriate choice of arbitrary functions and constants. Eventually, profiles show single soliton, elastic multisolitons, quasi periodic, parabolic and asymptotic nature of solutions.

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Explicit exact solutions for (2+1)-dimensional Boiti–Leon–Pempinelli equation

Cited by 21 publications

References 20 publications

Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation

Application of the Exp-function method to the (2+1)-dimensional Boiti–Leon–Pempinelli equation using symbolic computation

A series of new exact solutions of nonlinear evolution equations

Some more similarity solutions of the(2+1)-dimensional BLP system

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