%A Omel'yanov, George %D 2018 %T Collision of solitons for a nonhomogeneous version of the KdV equation %K %X We consider KdV-type equations with C 1 nonhomogeneous nonlinearities and small dispersion " . The first result consists of the conclusion that, in the leading term with respect to " , the solitary waves in this model interact like KdV solitons. Next, it turned out that there exists a very interesting scenario of instability in which the short-wave soliton remains stable whereas a small long-wave part, generated by perturbations of original equation, turns to be unstable, growing and destroying the leading term. At the same time, such perturbation can eliminate the collision of solitons. %U https://esmed.org/MRA/qpr/article/view/1632 %J Quarterly Physics Review %0 Journal Article %R 10.18103/qpr.v4i1.1632 %V 4 %N 1 %@ 2572-701X %8 2018-01-01