Mathematica Eterna
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Two types of traveling wave solutions of a KdV-like advection-dispersion equation

Xinghua Fan and Jiuli Yin

We present a KdV-like 2-parameter equation ut + (3(1 − δ)u + (δ + 1)uxx ux )ux = ϵuxxx. By using the dynamical system method, existence of different traveling wave solutions are discussed, including smooth solitary wave solution of with bell type, solitary wave solutions of valley type and peakon wave solution of valley type. Numerical integration are used to shown the different types of solutions.