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Math. Comput. Appl. 2014, 19(3), 194-207; doi:10.3390/mca19030194

New Exact Analytical Solutions for the General KdV Equation with Variable Coefficients

1
Faculty of Science, Jiangsu University, 212013, Zhenjiang, Jiangsu, PR China
2
Department of Basic Courses, Nanjing Institute of Technology, 211167,Nanjing, Jiangsu, PR Chin
*
Authors to whom correspondence should be addressed.
Published: 1 December 2014
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Abstract

In this paper, a general algebraic method based on the generalized Jacobi elliptic functions expansion method, the improved general mapping deformation method and the extended auxiliary function method with computerized symbolic computation is proposed to construct more new exact solutions of a generalized KdV equation with variable coefficients. As a result, eight families of new generalized Jacobi elliptic function wave solutions and Weierstrass elliptic function solutions of the equation are obtained by using this method, some of these solutions are degenerated to soliton-like solutions, trigonometric function solutions in the limit cases when the modulus of the Jacobi elliptic functions m → 1 or 0, which shows that the general method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear partial differential equations arising in mathematical physics.
Keywords: generalized KdV equation with variable coefficients; general algebraic method; exact solutions; generalized Jacobi elliptic function wave-like solutions generalized KdV equation with variable coefficients; general algebraic method; exact solutions; generalized Jacobi elliptic function wave-like solutions
This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. (CC BY 4.0).

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MDPI and ACS Style

Hong, B.-J.; Lu, D.-C. New Exact Analytical Solutions for the General KdV Equation with Variable Coefficients. Math. Comput. Appl. 2014, 19, 194-207.

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