Theoretical Mathematics & Applications

Analytic Solutions for A New Kind of Auto-Coupled KdV Equation with Variable Coefficients

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• Abstract

  In this paper, we apply the extended variable-coefficient mapping method to discuss a new kind of auto-coupled KdV equation with variable coefficients. By solving nonlinear differential algebraic equations which are derived from nonlinear evolution equations, many Jacobi elliptic function solutions, hyperbolic function solutions and trigonometric periodic solutions for the auto-coupled KdV equation with variable coefficients are derived. By selecting the appropriate parameter values, some exact solutions of the other forms are also obtained.