Abstract
A new model equation is proposed for simulating unidirectional wave propagation in nonlinear media with dispersion. This model equation is a one-dimensional evolutionary partial differential equation that is obtained by coupling the generalized Korteweg–de Vries (gKdV) equation, which includes a nonlinear term of any order and cubic dispersion, with the quintic regularized long wave (qRLW) equation, which includes fifth-order dispersion. Exact solitary wave solutions are derived for this model equation. These analytical solutions are obtained for any order of the nonlinear term and for any given values of the coefficients of the cubic and quintic dispersive terms. Analytical expressions for three conservation laws and for three invariants of motion for solitary wave solutions of this new equation are also derived.
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