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2005•Journal of Luoyang Institute of TechnologyRequires access

Solution for KdV Equation

Xiang Li

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Abstract

A new method of solving nonlinear KdV equation is introduced. By using the homogeneous balance principle (HBP) and the F-expansion method proposed recently, abundant exact solutions expressed by ellipticfunction, hyperbolic function, and trigonometric function for KdV equation are obtained, and the exact solutions whichinclude positive and negative power items are new. The method can be applied to solve more nonlinear partialdifferential equations.

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What this paper is about

A new method of solving nonlinear KdV equation is introduced. By using the homogeneous balance principle (HBP) and the F-expansion method proposed recently, abundant exact solutions expressed by ellipticfunction, hyperbolic function, and trigonometric function for KdV equation are obtained, and the exact solutions whichinclude positive and negative power items are new. The method can be applied to solve more nonlinear partialdifferential equations.

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Available abstract

A new method of solving nonlinear KdV equation is introduced. By using the homogeneous balance principle (HBP) and the F-expansion method proposed recently, abundant exact solutions expressed by ellipticfunction, hyperbolic function, and trigonometric function for KdV equation are obtained, and the exact solutions whichinclude positive and negative power items are new. The method can be applied to solve more nonlinear partialdifferential equations.

Key concepts: Korteweg–de Vries equation, Hyperbolic function, Mathematics, Trigonometric functions, Nonlinear system, Trigonometry, Homogeneous, Mathematical analysis

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