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1
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Exact Periodic Wave Solutions to the Nizhnik-Novikov-Veselov Equation

100%
Peng Y.
Acta Physica Polonica A
|
2004
|
vol. 105
|
issue 5
417-424
EN
Exact periodic wave solutions to the Nizhnik-Novikov-Veselov equation are obtained by means of the modified mapping method. Limit cases are studied and new solitary wave solutions and trigonometric periodic wave solutions are found.
2
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Exact Periodic Wave Solutions of Two Types of Modified Boussinesq Equations

100%
Peng Y.
Acta Physica Polonica A
|
2003
|
vol. 103
|
issue 5
417-421
EN
Exact periodic wave solutions to two types of modified Boussinesq equations are obtained by the use of the Jacobi elliptic function method in a unified form. Some new, general solitary wave solutions are presented.
3
Content available remote

Exact Travelling Wave Solutions for a Modified Zakharov-Kuznetsov Equation

100%
Peng Y.
Acta Physica Polonica A
|
2009
|
vol. 115
|
issue 3
609-612
EN
The extended mapping method is developed to study the traveling wave solution for a modied Zakharov-Kuznetsov equation. A variety of traveling periodic wave solutions in terms of the Jacobi elliptic functions are obtained. Limit cases are studied, and solitary wave solutions are got.
4
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The Variable Separation Method and Exact Jacobi Elliptic Function Solutions for the Nizhnik-Novikov-Veselov Equation

100%
Peng Y.
Acta Physica Polonica A
|
2006
|
vol. 110
|
issue 1
3-9
EN
Based on the singular structure analysis, the variable separation method is proposed for the Nizhnik-Novikov-Veselov equation to obtain a general functional separation solution containing three arbitrary functions. Choosing these arbitrary functions to be the Jacobi elliptic functions, a diversity of elliptic function solutions may be obtained for the equation of interest. The interaction property of the waves is numerically studied. The long wave limit gives the new type of localized coherent structures.
5
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Exact Solutions and Localized Structures for a (3+1)-Dimensional Burgers Equation

100%
Peng Y.
Acta Physica Polonica A
|
2012
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vol. 122
|
issue 1
20-24
EN
A (3+1)-dimensional Burgers equation is studied by the singular manifold method. By choosing different seed solutions, auto-Bäcklund transformation, the Cole-Hopf transformation and a functional separation exact solution containing two low dimensional arbitrary functions are obtained for the equation in question. Some interesting localized coherent structures are given and their interaction properties are numerically studied. Some new nonlinear phenomena are reported.
6
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Exact Travelling Wave Solutions to the (3+1)-Dimensional Kadomtsev-Petviashvili Equation

63%
Peng Y., Krishnan E.
Acta Physica Polonica A
|
2005
|
vol. 108
|
issue 3
421-428
EN
Exact travelling wave solutions in terms of the Jacobi elliptic functions are obtained to the (3+1)-dimensional Kadomtsev-Petviashvili equation by means of the extended mapping method. Limit cases are studied, and new solitary wave solutions and trigonometric periodic wave solutions are got. The method is applicable to a large variety of nonlinear partial differential equations.
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