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Explicit and exact solutions for a generalized long–short wave resonance equations with strong nonlinear term

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  • Shang, Yadong

Abstract

In this paper, the evolution equations with strong nonlinear term describing the resonance interaction between the long wave and the short wave are studied. Firstly, based on the qualitative theory and bifurcation theory of planar dynamical systems, all of the explicit and exact solutions of solitary waves are obtained by qualitative seeking the homoclinic and heteroclinic orbits for a class of Liénard equations. Then the singular travelling wave solutions, periodic travelling wave solutions of triangle functions type are also obtained on the basis of the relationships between the hyperbolic functions and that between the hyperbolic functions with the triangle functions. The varieties of structure of exact solutions of the generalized long–short wave equation with strong nonlinear term are illustrated. The methods presented here also suitable for obtaining exact solutions of nonlinear wave equations in multidimensions.

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  • Shang, Yadong, 2005. "Explicit and exact solutions for a generalized long–short wave resonance equations with strong nonlinear term," Chaos, Solitons & Fractals, Elsevier, vol. 26(2), pages 527-539.
    • Handle: RePEc:eee:chsofr:v:26:y:2005:i:2:p:527-539
    DOI: 10.1016/j.chaos.2005.01.066
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    Cited by:

    1. Yusufoğlu, Elcin & Bekir, Ahmet, 2008. "Exact solutions of coupled nonlinear evolution equations," Chaos, Solitons & Fractals, Elsevier, vol. 37(3), pages 842-848.
    2. Shang, Yadong, 2008. "The extended hyperbolic function method and exact solutions of the long–short wave resonance equations," Chaos, Solitons & Fractals, Elsevier, vol. 36(3), pages 762-771.

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